*BP's US depositary shares rebound by 11 per cent

*Anadarko, Transocean shares also jump

*UK's Cameron to discuss spill with Obama this weekend

*Cameron pledges help but understands US frustration

*US Attorney General says will ensure BP pays for spill

*Obama wants to update US laws to protect Gulf coast

Kabul/Houston - British Prime Minister David Cameron offered on Thursday to help deal with BP Plc's Gulf of Mexico oil spill, saying he would take it up with US President Barack Obama, as the beleaguered company's shares rebounded from 14-year lows.

It was the first time that Cameron had spoken publicly about the crisis. Cameron, who took office in May and is under growing pressure domestically to stand up for the British energy company, is due to talk to Obama by telephone this weekend.

Obama has been sharply critical of BP and the two leaders' conversation will have to seek a delicate balance between domestic pressures and long-standing US-British ties.

Obama said after meeting with Republican and Democratic congressional leaders at the White House that he wanted to update US pollution laws to ensure that victims of the oil spill are fully compensated. Obama also met with relatives of the 11 workers killed in the explosion of an offshore oil rig on April 20 that triggered the disaster.

BP pleaded for patience from Americans frustrated about the spill, the worst in US history and now in its 52nd day. But the Obama administration kept up the heat, saying it would make sure BP paid all damages and cleanup costs.

The spill has soiled 190km of US Gulf coastline, including wildlife refuges in Louisiana and barrier islands in Mississippi and Alabama. It threatens multibillion-dollar fishing and tourist industries.

In another sign the spill is spreading, heavier concentrations of oil began washing up on Florida seashores starting late on Wednesday. Until then, debris from the spill had been limited to relatively small tar balls.

BP was the second most active stock on the New York Stock Exchange as shares rebounded by more than 11 per cent by 3:15pm ET (0715 NZT). It took a 16 per cent dive to a 14-year-low on Wednesday amid concerns over BP's ability to meet mounting costs.

"The stock is obviously volatile as investors try to wager on the outcome of the Gulf oil spill," said Jud Pyle, chief investment strategist at Options News Network, a division of option market maker PEAK6 Investments in Chicago.

Analysts said the company's improved performance was partly due to speculation that PetroChina, Asia's top oil and gas firm, was considering making a bid for BP.

Shares in Anadarko Petroleum Corp and Transocean Ltd, two companies involved in the well, also jumped on Thursday. In London trading, BP stocks sank to their lowest level since 1997 before bouncing off their lows and closing 6.7 per cent down.

Illustrating the extent of investor concerns about BP, the cost of insuring its AA-rated debt traded for a time at levels normally associated with "junk" status.

After Wednesday's battering in New York, BP had lost more than half its market value since the crisis began.

"BP notes the fall in its share price in US trading last night. The company is not aware of any reason which justifies this share price movement," BP said in a statement on Thursday.

In Britain, business leaders urged the government to defend BP - the biggest single payer of dividends among UK listed companies - against US threats to expand the company's liabilities for the spill and pressure from the United States for it to suspend payment of its quarterly dividend.

Cameron, speaking on a visit to Afghanistan's capital Kabul, said, "This is an environmental catastrophe. BP needs to do everything it can to deal with the situation, and the UK government stands ready to help."

He added, "I completely understand the US government's frustration. The most important thing is to try to mitigate the effects and get to grips with the problem. It's something I will discuss with the American president when we next talk."

A British government spokesman said Cameron will talk to Obama on the subject this weekend in their first discussion since speaking when Cameron first took office.

White House spokesman Robert Gibbs said he did not believe the BP oil spill would affect US-British ties.

BP said it was capturing more oil from the deep-sea well. It is still not known, though, how much oil is gushing out.

BP Chief Operating Officer Doug Suttles said the company is doing everything it could to contain and clean up the spill.

"It's very difficult for people to believe that right now, and I know that, but I would just ask, just give us a chance," he told CNN. "We've got to get this job done. We've got to get this well killed."

The Obama administration has markedly toughened its rhetoric toward the company in recent days, reflecting US public anger over the oil giant's handling of the spill.

US Attorney General Eric Holder said on Thursday that the "American people will not pay a dime" for the clean-up of the Gulf region and pledged to hold BP financially responsible.

A senior Democratic politician joined calls from US lawmakers for BP to suspend dividend payments. Asked if BP should do this, US House of Representatives Speaker Nancy Pelosi said: "Yes, of course, and that would be their best public relations instead of taking out all these ads."

Lawmakers will likely press BP chief executive Tony Hayward on the issue when he testifies for the first time at a congressional hearing on the spill on June 17.

The White House said it was not ruling out the possibility that Obama would meet with BP executives on the spill.

BP said in written testimony to a Senate subcommittee on Thursday that it had paid half of the 39,000 claims that had been filed so far, totalling more than $53 million.

One of the world's largest corporate giants, BP said it had the financial flexibility to deal with liabilities related to the spill, which to date had cost it around $1.43 billion.

Restructuring experts agree that by running the numbers alone, BP looks able to handle the financial damage.

BP's latest effort to contain the spill involves placing a containment cap with a seal on a deep-sea pipe from which the oil is gushing into the Gulf of Mexico.

It said on Thursday the cap system had collected 15,800 barrels (2,500,000 litres) in the previous 24-hour period. The cumulative total since the system was installed last week has reached 73,324 barrels (11,660,000 litres), according to BP figures.

One third of the Gulf's federal waters remains closed to fishing as a result of the spill.

Gulf Coast residents have complained about BP's handling of damage claims related to the spill, saying they are paying too little, too slowly.