Exhibit 10(xx)

SECOND AMENDMENT

TO

REGISTRATION RIGHTS AGREEMENT

This SECOND AMENDMENT TO REGISTRATION RIGHTS AGREEMENT (this “Amendment”) is made and entered into this 23^rd day of June, 2010, by and among Magellan Petroleum Corporation, a Delaware corporation (the “Company”), Young Energy Prize S.A., a Luxembourg corporation (“YEP”), and ECP Fund, SICAV-FIS, a Luxembourg entity formerly known as YEP I, SICAV-FIS (“Fund”). This Amendment amends the Registration Rights Agreement dated as of July 9, 2009, as amended on October 14, 2009 (the “Registration Rights Agreement”), among the Company, YEP and Fund. Capitalized terms used but not otherwise defined in this Amendment shall have the meanings given to such terms in the Registration Rights Agreement. The Company, YEP and Fund are collectively the “Parties” hereunder, and each of them individually is a “Party.”

WHEREAS, the Parties desire to amend the Registration Rights Agreement as set forth herein; and

WHEREAS, Section 7(a) of the Registration Rights Agreement provides that the Registration Rights Agreement may be amended only by a writing signed by the Company, YEP and Fund.

NOW, THEREFORE, in consideration of the mutual covenants, agreements and for other good and valuable consideration, the receipt and adequacy of which is hereby acknowledged, the Parties hereby agree as follows:

1. Amendment of Registration Rights Agreement.

(a) The definition of “Warrant” in Section 1 of the Registration Rights Agreement shall be amended to read in its entirety as follows:

“Warrant” means the warrant to purchase shares of Common Stock issued to the Investor on July 9, 2009, as the same was amended on March 11, 2010 and as may be amended and restated from time to time.

2. Effect of this Amendment. Except as specifically amended as set forth herein, each term and condition of the Registration Rights Agreement shall continue in full force and effect.

3. Counterparts; Facsimile Signatures. This Amendment may be executed or consented to in counterparts, each of which shall be deemed an original and all of which taken together shall constitute one and the same instrument. This Amendment may be executed and delivered by facsimile or electronically and, upon such delivery, the facsimile or electronically transmitted signature will be deemed to have the same effect as if the original signature had been delivered to the other party.

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The parties have caused this Amendment to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.