BP executives have met US President Barack Obama at the White House after he vowed to make the oil company pay for the Gulf of Mexico oil spill.
In his first Oval Office address to the US as president, Mr Obama said he would tell BP's chairman the firm must set up a fund to compensate those affected.
Oil has been leaking into the Gulf since a drilling rig leased by BP blew up on 20 April, killing 11 workers.
BP has been accused of failing to follow proper procedures.
As oil has washed ashore in Gulf coast states, affecting businesses and wildlife, the rhetoric from US politicians has become increasingly bitter and the firm's share price has tumbled, with billions of dollars being wiped off its value.
Mr Obama initially invited BP chairman Carl-Henric Svanberg to the White House meeting.
He was accompanied on Wednesday by group chief executive, Briton Tony Hayward, who has been the public face of the crisis and has come in for strong criticism in the US.
BP America president Lamar McKay, managing director Robert Dudley and legal representatives also accompanied Mr Svanberg, reports say.
The meeting was Mr Obama's first face-to-face talks with them since the oil leak began.
"I will meet with the chairman of BP and inform him that he is to set aside whatever resources are required to compensate the workers and business owners who have been harmed as a result of his company's recklessness," Mr Obama said in his Tuesday night address from the White House's Oval Office.
"And this fund will not be controlled by BP. In order to ensure that all legitimate claims are paid out in a fair and timely manner, the account must and will be administered by an independent third party."
In response to the speech, BP said in a statement that it shared Mr Obama's goal of cleaning up the oil spill and helping the people affected by it.
The firm said it was looking forward to Wednesday's meeting "for a constructive discussion about how best to achieve these mutual goals".
In the UK, Prime Minister David Cameron told the BBC that while BP would pay "reasonable" compensation claims, the firm needed "certainty" over the level of its liabilities.
"This is BP's worry, that there won't be claims entertained that are three or four times removed from the oil spill," Mr Cameron said.
Estimates of how much oil is gushing out of the well have again risen dramatically.
A government panel of scientists now believes 35,000-60,000 barrels are leaking each day, up from its estimate last week of 20,000-40,000.
BP managed to place a cap over the leaking oil pipe earlier this month, and is now collecting some of the oil.
On Wednesday the company said it had begun operating a second containment system designed to bring oil and gas to the surface for burning, in an effort to increase the amount of oil that can be dealt with each day.
Clean energy call
In his address, Mr Obama described the spill as an assault on the shores and citizens of the US that tested the limits of human technology.
"We will fight this spill with everything we've got for as long it takes," he said.
And he said it demonstrated the need to end the US "addiction" to fossil fuels and embark on a future fuelled by clean energy.
"I say we can't afford not to change how we produce and use energy - because the long-term costs to our economy, our national security, and our environment are far greater," he said.
But he gave few details and made no pledges about specific legislation, instead promising to look at ideas from Republicans and Democrats on the issue.
Presidents use Oval Office addresses for what they regard as vital national issues.
The speech came as opinion polls suggest a majority of Americans disapprove of how Mr Obama has handled the crisis - the worst environmental disaster in US history.
The Republicans were quick to criticise the address, with party chairman Michael Steele accusing Mr Obama of exploiting the crisis for his own political gain.
You can follow the testimony of BP chief executive Tony Hayward when he appears before a US Congress committee on the BBC News website on Thursday 17 June, from 1400GMT (1000 EST).