Britain and the US have agreed that they want a "strong and stable" BP, as the oil company faces intense pressure over the Gulf of Mexico oil leak.
President Barack Obama and UK Prime Minister David Cameron discussed BP's problems at the G20 summit in Canada.
They agreed that BP must meet its clean-up obligations, but also that it was in both countries' interests that the company remained a viable business.
BP will be hoping the talks put an end to political attacks on the company.
Officials in the US administration have criticised BP's response to the spillage, and mounted strong attacks on chief executive Tony Hayward.
The criticism has spooked investors, who were already worried about the mounting costs of the clean-up operation.
A Downing Street statement issued after the meeting between Mr Obama and Mr Cameron, said: "The leaders agreed that BP should meet its obligations to cap the leak, clean up the damage and meet legitimate compensations.
"They also agreed that it was to both countries' advantage for BP to remain a strong and stable company."
There was no immediate official response from Washington, though a senior US official emphasised to reporters at the summit that BP's obligations "have got to be met".
Shares in BP plunged again last week amid speculation that the company may have to seek extra funds to pay for its oil spill costs.
On Friday the shares closed down more than 8% at 298.36p, hitting a 14-year low.
In a note to investors, trading house Nomura said pressure was growing on the company to "assure sufficient funding" to stop the spill.
Earlier BP said that its costs linked to the Gulf of Mexico oil disaster had risen to $2.35bn (£1.57bn).
The total costs, including compensation claims, are expected to be much higher.
"We consider that equity linked financing - perhaps backed by sovereign wealth - could prove the attractive short-term solution," said Nomura,
It added that BP's perceived need for more money was damaging the company in the eyes of investors.
BP's share price has more than halved since the oil disaster began in April, wiping about $90bn off the value of the company.
Investors are comfortable that BP is big and profitable enough to manage the clean-up costs - it made an annual profit of nearly $14bn last year.
However, there is more uncertainty over the impact that legal action and compensation claims could have.
BP is still pressing ahead with operations to collect some of the oil and gas still leaking from the oil well on the ocean floor.
It said piping oil to two vessels above was collecting about 17,000 barrels of oil a day.
Meanwhile work on the drilling of relief wells, designed to stop the leak, is continuing.
The first well is not due to be completed until early August.