Barack Obama and David Cameron said stricken oil giant BP should "remain a strong and stable company".
Speaking at the G20 summit, the leaders said the company should "meet its obligations to cap the leak, clean up the damage and meet legitimate compensation claims," the Telegraph reports.
However, they added "it was to both countries' advantage for BP to remain a strong and stable company".
Their discussions come amid growing concerns BP will never recover from the Deepwater Horizon disaster.
Shares in the company dropped to a 14-year low on Friday, down 6.4% to 298.36p, knocking 15 points off the FTSE 100 index of blue-chip shares.
Almost £66bn has been wiped from the value of the company since the rig explosion on April 20 and subsequent leak, more than halving BP's market cap.
However, there could be a slight recovery this week as forecasts suggest tropical storm Alex will not hit the area where repairs are taking place.
BP shares partly recouped some of last week's losses, up 1.56% to 309.35p in early trading this morning.
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