* Spill flow rate may be much higher than thought
* BP's U.S. depositary shares rebound by 12 percent
* UK's Cameron to discuss spill with Obama this weekend
* Mexico expects impact, considers ways to sue BP
* Obama invites BP chairman to White House (Adds analyst comment, turtle toll, edits)
By Kristen Hays and Chris Baltimore
HOUSTON, June 10 (Reuters) - U.S. government scientists on Thursday doubled their estimate of the amount of oil gushing out of a ruptured Gulf of Mexico oil well as British energy giant BP (BP.L) (BP.N) scrambled to stem the leak.
The news that the flow rate may be as high 40,000 barrels (1.68 million gallons/6.36 million liters) per day came after U.S. markets closed.
BP shares closed 6.65 percent down in London at 365.50 pence while in New York they rebounded from 14-year lows to end 12.3 percent higher at $32.78.
President Barack Obama has invited BP Chairman Carl-Henric Svanberg to the White House next Wednesday to discuss the spill, The White House said on Thursday. [ID:nN10260931]
BP has come under increased pressure from the Obama administration in recent days and on Thursday British Prime Minister David Cameron said Britain stood ready to help the British company deal with the spill. [ID:nLDE659160]
Speaking during a visit to Afghanistan, Cameron said he would take up the matter with Obama when they speak in the next few days. It was the first time Cameron made a public comment about the spill.
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Neighboring Mexico also entered the fray. It expects oil from BP Plc's damaged Gulf of Mexico well to reach its shores by December, and is considering how to sue the company for any environmental damage, Mexico's environment minister told Reuters. [ID:nN10229727]
Environment Minister Juan Elvira said Mexico is trying to stock up on oil booms and netting, a tough task because the United States has used up most of the gear available to protect its coastline, to try to capture oil that will start drifting south when sea currents change in October.
The spill, already the worst in U.S. history, may well be much bigger than many had thought.
U.S. scientists said on Thursday that between 20,000 and 40,000 barrels (840,000 and 1.7 million gallons/3.2 million and 6.4 million litres) of oil flowed from the well before June 3, when BP's remotely operated robots sawed through an underwater pipe to clear the way for a capping procedure.
U.S. Interior Secretary Ken Salazar told a congressional panel on Wednesday that the cut may have increased the rate by 4 to 5 percent.
Based on a rate of 40,000 barrels per day, the stricken well could have spewed as much as 2 million barrels (84 million gallons/317 million of liters) of oil since it ruptured on April 20 -- eight times the amount that the Exxon Valdez spilled into Prince William Sound in Alaska in 1989.
BP says it has collected 73,324 barrels (3.1 million gallons/11,7 million litres) of oil since installing the capping system.
The new estimates, in which BP had no input, could have huge financial implications.
"Any EPA (Environmental Protection Agency) fines would be on a per barrel basis, so the new numbers would not be good for any company held responsible," said one oil analyst based in New York who declined to be named.
Under the Clean Water Act, BP and others could be exposed to fines up to $4,300 for every barrel leaked into the gulf, according to legal experts and official documents.
The wide variation in the estimates points to the difficulty in estimating a flow that is 1 mile (1.6 km) beneath the surface and reachable only by remotely operated robots.
BP said it was capturing more of the torrent of oil that has spewed from the sea bottom since the April 20 rig explosion that killed 11 workers and set the disaster in motion.
But the almost 16,000 barrels it said on Thursday it had collected in the previous 24 hours is triple its initial estimates of the leak's flow rate, a point that will not be lost on critics as U.S. public and political anger mount.
As the spill spread, heavier concentrations of oil began washing up on Florida seashores late on Wednesday. Until then, debris from the spill had been limited in the state to relatively small tar balls.
The Obama administration has kept up the heat, saying it would make sure BP paid all damages and cleanup costs from the spill, which has has soiled 120 miles (190 km) of coastline and threatens lucrative fishing and tourist industries.
The crisis is now on the global diplomatic agenda for allies Britain and America.
Cameron, who took office in May and is under pressure domestically to stand up for the British company, is due to talk to Obama by telephone this weekend.
Obama has been sharply critical of BP. The two leaders' conversation will have to seek a delicate balance between domestic pressures and long-standing U.S.-British ties.
They will also take place against a backdrop of extreme market volatility for BP.
BP was the second-most active stock on the New York Stock Exchange on Thursday after taking a 16-percent dive to a 14-year-low the previous day 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 (0857.HK), Asia's top oil and gas firm, was considering making a bid for BP.
Images of oiled pelicans and other wildlife is further stoking public anger with both the government and BP.
A report released on Thursday by conservation group Oceana said that as of Tuesday, 36 oiled sea turtles have been found in the Gulf of Mexico and more than 300 additional sea turtles have been found dead or injured since the spill began.
"While scientists have not yet determined the cause of death for many of these turtles, this number is higher than usual," it said. It also noted that many of the dead or injured turtles would not wash up on beaches and so likely would never be found.
Additional reporting by Adrian Croft in Kabul, Mica Rosenberg in Mexico City, Alex Chambers in London, Matt Daily in New York, Timothy Gardner, Jeremy Pelofsky and Tom Dogget in Washington, Doris Frankel in Chicago, Anna Driver in Louisiana and Michael Peltier in Pensacola Beach, Florida; writing by Ed Stoddard and Ross Colvin; Editing by Sandra Maler