The leaders will discuss the crisis against a backdrop of public anger and political pressure on both sides of the Atlantic over the spill, which has fouled coastlines, closed rich fishing grounds and battered BP's share price.
BP has been the target of stinging attacks by the White House and its share price has gyrated on London and New York stock exchanges this week. Obama administration officials have threatened to increase BP's liabilities for the spill.
BP said it was considering suspending its dividend payments after U.S. politicians said it should pay all damage claims before making payouts to shareholders.
BP accounts for around 12 percent of all dividend payouts made by British companies, and suspension would hit British pension funds hard.
BP said the company's board would meet on Monday to discuss a range of issues -- it has been meeting weekly since the crisis started.
However, a source said a decision on the dividend may not be made until after BP Chairman Carl-Henric Svanberg has met Obama on Wednesday.
Concerns about the London-based energy giant's future -- it faces a U.S. government criminal and civil investigation and the prospect of a slew of lawsuits and hefty fines -- prompted Cameron and his finance minister on Friday to defend the firm.
The British prime minister was quoted by a spokesman as saying after speaking to Svanberg that "it is in everyone's interests that BP continues to be a financially strong and stable company".
The political backing helped the company's share price to claw back 7 percent in London.
Cameron, who took office in May, is due to speak to Obama by telephone call at 11 a.m. EDT (1500 GMT) on Saturday.
A Cameron spokeswoman said the call would be "statesmanlike and workmanlike". A White House official played down the BP focus, saying it would be just one of a number of issues raised.
The call will be a tricky test for the two leaders as both are under pressure to appear tough to voters at home.
Obama, criticized by some in the United States over his handling of the unfolding environmental and economic disaster that threatens lucrative fishing and tourist industries, has been seeking to direct public anger toward BP.
For his part, Cameron must show Britons that he is not caving in to pressure from his country's most powerful ally at a time when the two nations shoulder many common burdens and problems such as the bitter conflict in Afghanistan.
Business leaders, politicians and newspapers have pressed Cameron to defend BP against the Obama administration, whose criticism has been viewed domestically as Britain-bashing.
Efforts to contain the spill and clean up the oil were set to continue on Saturday with clean-up operations in gear as BP scrambled to siphon more crude from the well.
It has been capturing oil from the well since installing a containment system last week, though the well will not be sealed until August, when two relief wells now being drilled are due to be completed.
It remains unclear how much oil is pouring into the Gulf, but U.S. scientists this week doubled their estimate of the flow to as much as 40,000 barrels per day, stoking the ire of environmentalists.
"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 outside a wildlife cleaning facility in Buras, Louisiana.
The new estimates could have huge financial implications because under the U.S. 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 affected 120 miles (190 km) of U.S. coastline, will be $3-$6 billion, an analyst briefed by BP said in a research note on Friday.
The slick has fouled wildlife refuges in Louisiana, while tar balls have washed up on Florida's famous white beaches. One third of the Gulf's federal waters remain closed for fishing. (Additional reporting by Tom Bergin in London, Writing by Keith Weir in London and Ed Stoddard in Dallas; Editing by Alison Williams)