• Clean-up crews battle the slick, which has hit islands off Louisiana. Picture: AFP/Getty
The Prime Minister's phone conversation with Carl-Henric Svanberg – which took place as the PM returned from a visit to Afghanistan – came after scientists with the US Geological Survey doubled the estimate of the amount of oil gushing out of the ruptured well to 40,000 barrels a day.
Ahead of a phone discussion with US president Barack Obama today, Mr Cameron is being urged to defend BP by senior figures, including London mayor Boris Johnson, concerned about the "anti-British" tone of Mr Obama's attacks.
Earlier this week, Mr Obama – under pressure to show more emotion over the spill – told a TV interviewer that he knew "whose ass to kick" and said he would have sacked BP's chief executive, Tony Hayward.
Mr Svanberg has been summoned to meet Mr Obama on Wednesday, and the BP board will meet on Monday to decide whether to suspend or reduce a planned 10 billion dividend payout to shareholders.
The Swedish chairman visited Downing Street yesterday, where he met Chancellor George Osborne and officials, and spoke to Mr Cameron by phone. After the talks, Downing Street said: "The Prime Minister had a constructive call with Mr Svanberg.
"The Prime Minister explained he was frustrated and concerned about the environmental damage caused by the leak but made clear his view that BP is an economically important company in the UK, US and other countries. He said it is in everyone's interests that BP continues to be a financially strong and stable company.
"Mr Svanberg made clear that BP will continue to do all that it can to stop the oil spill, clean up the damage and meet all legitimate claims for compensation.
"The Prime Minister said that he would raise the issue – and discuss these points – in his call with President Obama."
Emerging from the talks, Mr Svanberg said: "I think we have done everything we can to try to fill the well and we have said we would do everything expected from us in cleaning up the beach, taking care of all the claims and learn from this incident and make deep-sea drilling an even safer place." He refused to comment on the dividend issue or Mr Obama's comments.
Mr Johnson has demanded an end to the "beating up" of the oil firm, urging Mr Obama's administration to avoid "name-calling and buck-passing". BP was paying "a very, very heavy price" for what had been an accident, said Mr Johnson, pointing out that UK pension funds had a "huge exposure" to the oil giant. The firm is estimated to account for 1 in every 7 of dividends paid to British shareholders.
Meanwhile, in an open letter to the president, the chairman of insurance giant Royal Sun Alliance, John Napier, warned Mr Obama's criticism was "unstatesmanlike" and lacked "balance".
However, No 10 stressed that today's call to Mr Obama was "routine" and not an emergency response to crisis.
The National Association of Pension Funds played down the risk to UK pensions if BP cuts dividends. Chief executive Joanne Segars said BP's long-term future was more important.
Former trade minister Lord Jones said people would like to see Mr Cameron "be a bit more forceful". He added: "
I don't want BP falling foul of domestic pork-barrel politics with mid-term elections coming up."
The 20 April blast on the Deepwater Horizon rig claimed the lives of 11 oil workers .