AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT

Exhibit 10.1

EXECUTION VERSION

AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT

between

UNITED ENERGY GROUP LIMITED

and

TRANSMERIDIAN EXPLORATION INCORPORATED

Dated as of June 11, 2008 and Amended and Restated as of September 22, 2008

TABLE OF CONTENTS

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AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT, dated as of June 11, 2008 and amended and restated as of September 22, 2008 (this “ Agreement ”), by and between UNITED ENERGY GROUP LIMITED, an exempted company with limited liability existing under the laws of Bermuda (“ Investor ”), and TRANSMERIDIAN EXPLORATION INCORPORATED, a Delaware corporation (the “ Company ”). All capitalized terms used but not defined herein shall have the respective meanings ascribed thereto in the Investment Agreement (as defined below).

WHEREAS, Investor and the Company entered into an Investor Rights Agreement on June 11, 2008 (the “ Prior Agreement ”) and desire to amend and restate the Prior Agreement in its entirety with this Agreement.

WHEREAS, Investor and the Key Senior Preferred Stockholders have entered into those certain Senior Preferred Stock Purchase Agreements, dated as of June 11, 2008, pursuant to which Investor has agreed to purchase from each of the Key Senior Preferred Stockholders, and each Key Senior Preferred Stockholder has agreed to sell to Investor, all of the shares of the Senior Preferred Stock owned of record and beneficially by such Key Senior Preferred Stockholder, upon the terms and subject to the conditions set forth in the Senior Preferred Stock Purchase Agreements (collectively, the “ Rollover Transactions ”);

WHEREAS, Investor and the Key Junior Preferred Stockholders have entered into that certain Junior Preferred Stock Purchase Agreement, dated as of June 11, 2008, pursuant to which Investor has agreed to purchase from each Key Junior Preferred Stockholder, and each Key Junior Preferred Stockholder has agreed to sell to Investor, all of the shares of the Junior Preferred Stock owned of record and beneficially by such Key Junior Preferred Stockholder, upon the terms and subject to the conditions set forth in the Junior Preferred Stock Purchase Agreement (the “ Sale and Purchase Transactions ”);

WHEREAS, Investor and the Company have entered into that certain Investment Agreement, dated as of June 11, 2008 and amended and restated as of September 22, 2008 (the “ Investment Agreement ”), pursuant to which (a) on August 4, 2008 Investor commenced a cash tender offer (the “ Tender Offer ”) to acquire the Remaining Shares of Senior Preferred Stock and the Remaining Shares of Junior Preferred Stock, and (b) on July 23, 2008, as requested by Investor, the Company and the 12% Senior Notes Issuer (i) commenced an offer to exchange New Senior Notes and the 12% Senior Notes Cash Payments for the 12% Senior Notes and (ii) concurrently with the exchange offer, are soliciting consents from holders of the 12% Senior Notes to adopt certain amendments to the Indenture, in each case upon the terms and subject to the conditions set forth in the Investment Agreement (such exchange offer and consent solicitation being collectively referred to herein as the “ Exchange Offer ”, and together with the Tender Offer, the “ Offers ”);

WHEREAS, pursuant to the Investment Agreement, upon the consummation of the Offers, the Rollover Transactions and the Sale and Purchase Transactions, the Company intends to issue to Investor (i) the Series B-1 Preferred Stock; (ii) the Series B-2 Preferred Stock; and (iii) the Mandatory Warrants and the Optional Warrants in exchange for (A) the Preferred Stock tendered pursuant to the Tender Offer; (B) the Senior Preferred Stock purchased by Investor pursuant to the Senior Preferred Stock Purchase Agreements; (C) the Junior Preferred Stock purchased by Investor pursuant to the Junior Preferred Stock Purchase Agreement; (D) the First Tranche Price; (E) the Second Tranche Price; and (F) the Additional Returns; and (b) a number of shares of Common Stock determined in accordance with Section 4.04 of the Investment Agreement and the Exchange Warrants in exchange for (x) the 12% Senior Notes and the New Senior Notes then held by Investor or any of its Affiliates and (y) that portion of the 12% Senior Notes Cash Payments funded by Investor, in each case upon the terms and subject to the conditions set forth in the Investment Agreement (collectively, the “ Swap ”);

WHEREAS, promptly after the Swap Closing, the Company intends to issue to Investor a number of shares of Common Stock to be determined pursuant to Section 4.04 of the Investment Agreement in exchange for that portion of the Senior Notes Repurchase Payment and the New Senior Notes Redemption Payment funded by Investor, upon the terms and subject to the conditions set forth herein (the “ Repurchase and Redemption Issuance ” and, together with the Swap, the Rollover Transactions, the Sale and Purchase Transactions and the Offers, the “ Transactions ”); and

WHEREAS, the parties hereto desire to enter into this Agreement to establish certain rights and obligations of Investor and the Company with respect to the New Preferred Stock and the Common Stock to be issued pursuant to the Investment Agreement and the Common Stock issuable upon the exercise of the Warrants.

NOW, THEREFORE, in consideration of the premises and the covenants hereinafter contained and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, and intending to be legally bound hereby, it is agreed as follows:

ARTICLE I

DEFINITIONS

SECTION 1.01 Certain Defined Terms . Unless otherwise defined herein, the terms below shall have the following meanings (such meanings being equally applicable to both the singular and plural form of the terms defined):

“ Certificate(s) of Designations ” means the Certificate of Designations with respect to the Series B-1 Preferred Stock and/or the Certificate of Designations with respect to the Series B-2 Preferred Stock, as the case may be.

“ Holder ” means Investor, and any transferee of Investor to whom Registrable Securities are permitted to be transferred in accordance with the terms of this Agreement and the Certificates of Designations, and, in each case, who continues to be entitled to the rights of a Holder hereunder.

“ Pro Rata Percentage ” means, for each class or type of securities being offered in an underwritten public offering, (i) the number of unregistered securities of such class or type held by a selling equity holder divided by (ii) the total number of unregistered securities of such class or type proposed to be sold by all selling equity holders.

“ Registrable Securities ” means (i) the New Preferred Stock and the Common Stock issuable upon conversion of any shares of the New Preferred Stock or upon exercise of any of the Warrants, and any shares of New Preferred Stock or Common Stock issued in lieu of cash dividends on the New Preferred Stock (ii) the Common Stock issued to the Investor pursuant to Sections 4.04(a) and (b) of the Investment Agreement; and (iii) any securities issuable or issued or distributed in respect of any of the New Preferred Stock or Common Stock identified in clauses (i) and (ii) by way of stock dividend or stock split or in connection with a combination of shares, recapitalization, reorganization, merger, consolidation or otherwise. For purposes of this Agreement, (A) Registrable Securities shall cease to be Registrable Securities when a Registration Statement covering such Registrable Securities has been declared effective under the Securities Act by the SEC and such Registrable Securities have been disposed of pursuant to such effective Registration Statement and (B) the Registrable Securities of a Holder shall not be deemed to be Registrable Securities at any time when the entire amount of such Registrable Securities proposed to be sold by such Holder in a single sale (i) constitute less than 1% of the then outstanding shares of Common Stock, (ii) are or, in the opinion of counsel satisfactory to the Company and such Holder, each in their reasonable judgment, may be, so distributed to the public pursuant to Rule 144 (or any successor provision then in effect) under the Securities Act in any three month period or (iii) any such Registrable Securities have been sold in a sale made pursuant to Rule 144 under the Securities Act (or any successor provision then in effect).

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“ Registration Statement ” means a Demand Registration Statement, Piggy-Back Registration Statement and/or Shelf Registration Statement, as the case may be.

SECTION 1.02 Additional Defined Terms . The following terms have the meanings set forth in the Section set forth opposite such term:

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ARTICLE II

REGISTRATION RIGHTS

SECTION 2.01 Demand Registration . (a) Upon receipt of a written request from a Holder holding at least 25% of the Registrable Securities at such time (on an as converted basis) requesting that the Company effect a registration (a “ Demand Registration ”) under the Securities Act covering all or part of the Registrable Securities which specifies the intended method or methods of disposition thereof, the Company shall promptly notify all Holders in writing of the receipt of such request and each such Holder, in lieu of exercising its rights under Section 2.04 hereof may elect (by written notice sent to the Company within ten (10) Business Days from the date of such Holder’s receipt of the aforementioned notice from the Company) to have all or part of such Holder’s Registrable Securities included in such registration thereof pursuant to this Section 2.01, and such Holder shall specify in such notice the number of Registrable Securities that such Holder elects to include in such registration. Thereupon the Company shall, as expeditiously as is possible, but in any event no later than thirty (30) days (excluding any days which occur during a permitted Blackout Period under Section 2.05 below) after receipt of a written request for a Demand Registration, file with the SEC and use its reasonable best efforts to cause to be declared effective, a registration statement (a “ Demand Registration Statement ”) relating to all shares of Registrable Securities which the Company has been so requested to register by such Holders (“ Participating Demand Holders ”) for sale, to the extent required to permit the disposition (in accordance with the intended method or methods thereof, as aforesaid) of the Registrable Securities so registered.

(b) If the Participating Demand Holders in a Demand Registration relating to a public offering holding a majority in interest of Registrable Securities (on an as converted basis) for which such Demand Registration was requested request that the offering be underwritten with a managing underwriter selected in the manner set forth in Section 2.13 below and such managing underwriter of such Demand Registration advises the Company in writing that, in its opinion, the number of securities to be included in such offering is greater than the total number of securities which can be sold therein without having a material adverse effect on the distribution of such securities or otherwise having a material adverse effect on the marketability thereof (the “ Maximum Number of Securities ”), then the Company shall include in such Demand Registration the Registrable Securities that the Participating Demand Holders have requested to be registered thereunder only to the extent the number of such Registrable Securities does not exceed the Maximum Number of Securities. If such amount exceeds the Maximum Number of Securities, the number of Registrable Securities included in such Demand Registration shall be allocated among all of the Participating Demand Holders on a pro rata basis (based on the number of Registrable Securities held by each Participating Demand Holder). If the amount of such Registrable Securities does not exceed the Maximum Number of Securities, the Company may include in such Demand Registration any other securities of the Company held by other security holders of the Company in an amount not to exceed the difference between (i) the Maximum Number of Securities and (ii) the Registrable Securities which the Company has been requested to register by the Participating Demand Holders, as the Company may in its reasonable discretion determine or be obligated to allow, in an amount which together with the Registrable Securities included in such Demand Registration shall not exceed the Maximum Number of Securities.

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(c) Registrations under this Section 2.01 shall be on such appropriate form of the SEC (i) as shall be selected by the Company and (ii) as shall permit the disposition of the Registrable Securities in accordance with the intended method or methods of disposition specified in the applicable Holders’ request for such registration.

(d) Notwithstanding anything to the contrary contained herein, the Company shall not be required to prepare and file (i) more than two (2) Demand Registration Statements in any twelve-month period or (ii) any Demand Registration Statement within ninety (90) days following the date of effectiveness of any other Registration Statement.

SECTION 2.02 Shelf Registration . (a) Any Demand Registration Statement may be required by Participating Demand Holders constituting a majority of the Registrable Securities (on an as converted basis) for which such Demand Registration was requested to be in an appropriate form under the Securities Act (a “ Shelf Registration Statement ”) relating to any or all of the Registrable Securities in accordance with the methods and distribution set forth in the Shelf Registration Statement and Rule 415 under the Securities Act (the “ Shelf Registration ”).

(b) The Company shall use its reasonable best efforts to have such Shelf Registration Statement declared effective, subject to Section 2.05 below, and to keep such Shelf Registration Statement continuously effective, supplemented and amended to the extent necessary to ensure that it (i) is available for resales of Registrable Securities by such Holders; (ii) conforms with the requirements of this Agreement, the Securities Act and the policies, rules, regulations and other applicable requirements of the SEC as announced from time to time; and (iii) does not contain any untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary in order to make the statements therein, in light of the circumstances under which they were made, not misleading ( provided , however , that the Company shall have no such obligations or liabilities with respect to any written information pertaining to any Holder and furnished to the Company by or on behalf of such Holder specifically for inclusion therein), in each case until such time as all of the Registrable Securities covered by the Shelf Registration Statement (A) have been sold in the manner provided for therein and pursuant thereto, (B) have been distributed to the public pursuant to Rule 144 under the Securities Act (or any successor rule thereof), or (C) cease to be outstanding (the “ Shelf Registration Period ”). A request of a Demand Holder under this Section 2.02 shall be deemed to be a request for a Demand Registration for the purposes of Section 2.01(d).

(c) Registrations under this Section 2.02 shall be on such appropriate form of the SEC (i) as shall be selected by the Company and (ii) as shall permit the disposition of the Registrable Securities in accordance with the intended method or methods of disposition specified in the applicable Holders’ request for such registration.

SECTION 2.03 Limitations on Demand/Shelf Registrations . Holders shall be entitled to an aggregate of three (3) Registrations of Registrable Securities pursuant to Section 2.01 or Section 2.02 (each, a “ Demand for Registration ”); provided that a registration requested pursuant to Section 2.01 or Section 2.02 shall not be deemed to have been effected for purposes of this Section 2.03 unless (i) it has been declared effective by the SEC; (ii) it has remained effective for the period set forth in Section 2.06(a), subject to Section 2.05 and Section 2.06(i); and (iii) the offering of Registrable Securities pursuant to such registration is not subject to any

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stop order, injunction or other order or requirement of the SEC (for any reason other than the acts or omissions of Holders) unless such stop order, injunction or other order or requirement of the SEC has been withdrawn, vacated or otherwise removed.

SECTION 2.04 Piggy-Back Registration . (a) If the Company proposes to file on its behalf and/or on behalf of any holder of its securities (other than a Holder) a registration statement under the Securities Act on any form (other than a registration statement on Form S-4 or S-8 or any successor form for securities to be offered in a transaction of the type referred to in Rule 145 under the Securities Act or to employees of the Company pursuant to any employee benefit plan, respectively) for the registration of Common Stock or preferred stock that is convertible to Common Stock (a “ Piggy-Back Registration ”), it will give written notice to all Holders at least thirty (30) days before the initial filing with the SEC of such piggy-back registration statement (a “ Piggy-Back Registration Statement ”), which notice shall set forth the intended method of disposition of the securities proposed to be registered by the Company. The notice shall offer such Holders the opportunity to include in such filing such number of Registrable Securities as each such Holder may request.

(b) Each Holder desiring to have Registrable Securities registered under this Section 2.04 (“ Participating Piggy-Back Holders ”) shall advise the Company in writing within fifteen (15) days after the date of receipt of such offer from the Company, setting forth the amount of such Registrable Securities for which registration is requested. The Company shall thereupon include in such filing the number or amount of Registrable Securities for which registration is so requested, subject to paragraph (c) below, and shall use its reasonable best efforts to effect registration of such Registrable Securities under the Securities Act.

(c) If the Piggy-Back Registration relates to an underwritten public offering and the managing underwriter of such proposed public offering advises in writing that, in its opinion, the amount of Registrable Securities requested to be included in the Piggy-Back Registration in addition to the securities being registered by the Company would be greater than the Maximum Number of Securities (having the same meaning as defined in Section 2.01 but replacing the term “ Demand Registration ” with “ Piggy-Back Registration ”), then:

(i) In the event that the Company initiated the Piggy-Back Registration, the Company shall include in such Piggy-Back Registration first , the securities the Company proposes to register and second , the securities of all other selling equity holders, including the Participating Piggy-Back Holders, to be included in such Piggy-Back Registration in an amount which together with the securities the Company proposes to register, shall not exceed the Maximum Number of Securities, such amount to be allocated among such selling equity holders based on each such holder’s Pro Rata Percentage.

(ii) In the event any holder of securities of the Company (other than a Holder) initiated the Piggy-Back Registration, the Company shall include in such Piggy-Back Registration first , the securities such initiating equity holder proposes to register, second , the securities of any other selling equity holders (including Participating Piggy-Back Holders), in an amount which together with the securities the initiating equity holder proposes to register, shall not exceed the Maximum Number of Securities, such

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amount to be allocated among such other selling equity holders based on each such holder’s Pro Rata Percentage; and third , any securities the Company proposes to register, in an amount which, together with the securities the initiating equity holder and the other selling equity holders propose to register, shall not exceed the Maximum Number of Securities.

(d) The Company will not hereafter enter into any agreement that is inconsistent with the rights of priority provided in paragraph (c) above.

SECTION 2.05 Blackout Periods . The Company shall have the right to delay the filing or effectiveness, or in the case of a Shelf Registration Statement, to suspend the use, of a Registration Statement required pursuant to Section 2.01, Section 2.02 or Section 2.04 hereof during no more than two (2) periods aggregating to not more than forty-five (45) days in any twelve-month period (except as a result of a review of any post-effective amendment by the SEC before declaring any post-effective amendment to a Registration Statement effective, provided that the Company has used its reasonable best efforts to cause such post-effective amendment to be declared effective) (a “ Blackout Period ”) in the event that in the judgment of the Board, (i) there is a reasonable likelihood that such disclosure, or any other action to be taken in connection with the prospectus, would materially and adversely affect or interfere with any financing, acquisition, merger, disposition of assets (not in the ordinary course of business), corporate reorganization or other similar transaction in which the Company is engaged or in respect of which the Company proposes to engage in discussions or negotiations, or has proposed or taken a substantial step to commence, (ii) there is an event or state of facts relating to the Company which is material to the Company the disclosure of which would, in the reasonable judgment of the Company be adverse to its interests or (iii) it is required by law, rule, regulation or published release or interpretation of the SEC to supplement the Registration Statement or file a post-effective amendment to the Registration Statement in order to incorporate information into the Registration Statement for the purpose of (1) including in the Registration Statement any prospectus required under Section 10(a)(3) of the Securities Act; (2) reflecting in the prospectus included in the Registration Statement any facts or events arising after the effective date of the Registration Statement (or of the most-recent post-effective amendment) that, individually or in the aggregate, represents a fundamental change in the information set forth therein; or (3) including in the prospectus included in the Registration Statement any material information with respect to the plan of distribution not disclosed in the Registration Statement or any material change to such information; provided , however , that the Company shall delay during such Blackout Period the filing or effectiveness of any Registration Statement or suspend the use of any Registration Statement, as applicable, required pursuant to the registration rights of the holders of any securities of the Company. The Company shall promptly give the Holders written notice of such determination containing a general statement of the reasons for such postponement and an approximation of the anticipated delay.

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SECTION 2.06 Registration Procedures . If the Company is required by the provisions of Section 2.01, Section 2.02 or Section 2.04 to use its reasonable best efforts to effect the registration of any of its securities under the Securities Act, the Company will, as expeditiously as possible:

(a) prepare and file with the SEC a Registration Statement with respect to such securities and use its reasonable best efforts to cause such Registration Statement to become effective as promptly as practicable and to remain effective for a period of time required for the disposition of such securities by the holders (including the Holders) thereof but not to exceed thirty (30) days (except with respect to a Shelf Registration Statement which shall remain effective for the Shelf Registration Period); provided , however , that before filing such Registration Statement or any amendments or supplements thereto (including in each case all exhibits), the Company shall furnish the representatives of the Holders referred to in Section 2.06(m) copies of all documents proposed to be filed, which documents will be subject to the review of such Holders and their respective representatives. The Company shall not be deemed to have used its reasonable best efforts to keep a Registration Statement effective during the applicable period if it voluntarily takes any action that would result in the Holders of such Registrable Securities not being able to sell such Registrable Securities during that period, unless such action is required under applicable law or except to the extent contemplated by Section 2.05 or 2.06(i)(v);

(b) prepare and file with the SEC such amendments and supplements (including in each case all exhibits) to such Registration Statement and the prospectus used in connection therewith as may be necessary to keep such Registration Statement effective and to comply with the provisions of the Securities Act with respect to the sale or other disposition of all securities covered by such Registration Statement until the earlier of such time as all of such securities have been disposed of in a public offering or the expiration of thirty (30) days (except with respect to the Shelf Registration Statement, for which such period shall be the Shelf Registration Period);

(c) furnish to such selling security holders (including the Holders) such number of conformed copies of the applicable Registration Statement and each such amendment and supplement thereto (including in each case all exhibits), such copies of a summary prospectus or other prospectus, including a preliminary prospectus, in conformity with the requirements of the Securities Act, and such other documents, as such selling security holders (including the Holders) may reasonably request in order to facilitate the public sale or other disposition of the securities covered by such Registration Statement. The Company consents, subject to the provisions of this Agreement, to the use of the prospectus or any amendment or supplement thereto by each Holder participating in the offering and sale of the Registrable Securities covered by the prospectus, or any amendment or supplement thereto, included in the applicable Registration Statement;

(d) prior to any public offering of the securities pursuant to the applicable Registration Statement, register or qualify the securities covered by such Registration Statement under such other securities or blue sky laws of such jurisdictions within the United States as each Holder of such securities shall reasonably request, to keep such registration or qualification in effect for so long as such Registration Statement remains in effect, and to take any other action which may be reasonably necessary to enable such seller to consummate the disposition in such jurisdictions of the securities owned by such Holder, and do such other reasonable acts and things as may be required of it to enable such Holder to consummate the disposition in such jurisdiction of the securities covered by such Registration Statement; provided that the Company shall not be required to qualify generally to do business in any jurisdiction or to register as a broker or dealer in such jurisdiction where it would not otherwise be required to qualify but for this provision, or submit to the general service of process in any such jurisdiction;

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(e) furnish, at the request of any Holder requesting registration of Registrable Securities pursuant to Section 2.01, Section 2.02 or Section 2.04, if the method of distribution is by means of an underwriting, on the date