Exhibit 10.4

Young Energy Prize S.A.

Rives de Clausen, 26-28

L-2165 Luxembourg

February 17, 2011

Magellan Petroleum Corporation

7 Custom House Street

3rd Floor

Portland, ME 04101

Attn: William H. Hastings, President and CEO

Dear Bill,

Magellan Petroleum Corporation (“MPC”) and Young Energy Prize S.A. (“YEP”) entered into an Investment Agreement on February 11, 2011 (the “Investment Agreement”) pursuant to which, among other things, YEP has agreed to provide A$85,450,000 of funding (the “Acquisition Funding”) for the prospective acquisition by Magellan Petroleum Australia Limited (“MPAL”) of a forty percent ownership interest (the “Interest”) in the Evan Shoal natural gas resource (“Evans Shoal”) which prospective acquisition is pursuant to an Asset Sale Deed dated March 25, 2010 between MPAL and Santos Offshore Pty Ltd. (“Santos”), as amended by a Deed of Variation dated January 31, 2011 between MPAL and Santos (together the “Santos Agreement”). This letter sets forth additional agreements between MPC and YEP regarding the Investment Agreement.

1. Notwithstanding anything to the contrary contained in the Investment Agreement and the Santos Agreement, MPC, MPAL and YEP agree that YEP’s obligation to provide the Acquisition Funding pursuant to the Investment Agreement is subject to:

(a) The other owners of Evans Shoal having consented to the acquisition of the Interest by MPAL; and

(b) All other requirements and conditions for the acquisition of the Interest by MPAL set forth in the Santos Agreement having been satisfied or waived.

2. In the event that there is a closing of the acquisition of the Interest by MPAL, YEP and MPC shall equally share the payment (or reimbursement) of all third party out-of-pocket transaction costs (the “Costs”) associated with such acquisition incurred by each party,

including those related to the financing thereof (to include Costs related to the PIPE), provided that the share of such costs to be paid by YEP shall not exceed $3,500,000. Notwithstanding the foregoing however, in the event that there is not a closing of the acquisition of the Interest but there is a closing of the PIPE as set forth in paragraph 1 above, YEP shall not be obligated to pay any of the Costs and all Costs shall be paid by MPC. Each of MPC and YEP shall have the right to approve all material Costs, which approval shall not be unreasonably withheld.

3. The provisions of this letter agreement supersede any other letter agreement relating to the matters set forth herein, which other letter agreement shall be of no further force or effect.

Please indicate your acceptance of the terms and conditions of this letter by signing in the space indicated below.

Acknowledged and Accepted as of the date of this letter by: