Recent comments by the US president, including plans to make BP pay the salaries of oil industry workers who have been laid from other rigs since the April 20 disaster, have worried investors.
BP's share price plunged to a 14-year low after the US threatened to impose new penalties on the company, angered by the magnitude of the spill caused by the collapse of an rig following an explosion.
The company also faces a US government criminal and civil investigation, possibly resulting in a slew of lawsuits and hefty fines, which raised further concerns about the London-based company's future.
Cameron on Friday tried to defend the firm, saying after talks with Carl-Henric Svanberg, BP's Chairman, that "it is in everyone's interests that BP continues to be a financially strong and stable company".
Svanberg also met with George Osborne, Britain's finance minister, and other senior officials in Downing Street, and the company's share price rose by seven per cent by close of trade on Friday.
Prior to the meeting, Cameron, who took office in May, was under pressure to appear tough to voters at home, after the Obama administration's criticism of BP was viewed as Britain-bashing.
Obama has been seeking to direct public anger towards BP, after he was criticised by some in the US over his handling of the unfolding environmental and economic disaster.
The oil spill has seen huge amounts of oil wash up on the US Gulf coastline, threatening precious wildlife and local communities that rely on lucrative fishing and tourist industries.
Obama also demanded that BP scrap its shareholder dividend, as the total bill so far, including cleanup costs, reached $1.25bn with billions more in penalties expected.
Tony Hayward, BP's chief executive, said that they were considering all options on the dividend, "but no decision has been made".
Meanwhile, BP continued attempts to syphon more crude from the well, after new studies suggested that the amount of oil gushing into the ocean was double what was previously estimated.
Bob Deans of the Natural Resources Defence Council, an environmental group, said he was shocked by the new estimate of 40,000 barrels per day.
"We knew it was bad when BP was telling us 5,000 barrels a day. Now that we're up to as much as eight times that amount ... it's exponentially worse," Deans said.
The new estimates could have huge financial implications because under the US Clean Water Act, BP and others face fines up to $4,300 for every barrel of oil leaked.
BP expects the total bill for the clean-up of the spill, which has already affected 190km of US coastline, will be $3-$6 billion.
The slick has fouled wildlife refuges in Louisiana, while tar balls have washed up on Florida's famous white beaches.