Twice as much oil might have spewed out of the blown-out BP well in the Gulf of Mexico as previous estimated, scientists said Thursday.

A U.S. government-created task force, known as the Flow Rate Technical Group, said between 20,000 and 40,000 barrels of oil a day might have spilled out before a cap was installed on June 3.

Scientists had previously estimated about 12,000 to 19,000 barrels of oil a day had been leaking from the well since an oil rig exploded April 20. The U.S. government had put the estimate lower, at about 5,000 barrels per day.

"Our scientific analysis is still a work in progress," said Marcia McNutt, director of the U.S. Geological Survey, who released the newest estimates.

Obama meets dead rig workers' families

Meanwhile, U.S. President Barack Obama met Thursday afternoon with relatives of the 11 men who died when the BP-leased Deepwater Horizon oil rig exploded off the Louisiana coast.  Their bodies have not been found.

Obama visited with the relatives individually at the White House, offering his condolences and expressing his administration's support.

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Keith Jones, whose son Gordon Jones was killed in the BP well explosion, leaves the White House with a staff member on Thursday after meeting President Barack Obama. ((Alex Brandon/Associated Press))

He also vowed not to allow deepwater drilling until proper safety measures are in place, a White House statement said.

But the six-month moratorium has angered some politicians and workers, who say it will severely damage the industry.

"Mr. President, you were looking for someone's butt to kick," Charlotte Randolph, president of Lafourche Parish in Louisiana, said in pleading for the moratorium to end. "You're kicking ours."

The gathering at the White House was the first time Obama met with families of those who died in the explosion. Some families had said they've felt forgotten as attention has focused on the massive cleanup efforts.

Keith Jones, who lost his 28-year-old son, Gordon, was among those looking forward to meeting with Obama. On Thursday morning, he told CNN he thinks the president has done enough in the 52 days since the explosion but wanted to hear from him directly about what's being done to contain the spill and to provide benefits to the victims' families.

"I don't know what people expect him to do, if they expect him to go down and clean pelicans," Jones said. "I think that the criticism of the president that I've seen is from a public relations standpoint."

Changes to claims process

The visit by family members followed an intense meeting between Obama and congressional leaders, also at the White House.

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House Speaker Nancy Pelosi looks on as Obama makes a statement to reporters at the White House on Thursday. ((Charles Dharapak/Associated Press))

The response to the oil spill was at "the top our list," Obama said afterward. There was also "a frank conversation" about the adequacy of existing laws to support individuals and businesses affected by such disasters, he said.

"It's going to be important that … we update the laws to make sure that the people in the Gulf — the fishermen, the hotel owners, families — who are dependent for their livelihoods on the Gulf, that they are all made whole and that we are in a much better position to respond to any such crisis in the future," he said after the meeting.

White House officials have urged senior BP officials to be more "transparent, prompt and responsive" in the claims process, Tracy Wareing, of the Department of Homeland Security, told reporters Thursday.

The company has agreed to change the way it processes claims for compensation and will expedite payments, she said. It will also drop the current practice of waiting to make such payments until businesses have closed their books for each month.

Obama has visited the Louisiana coast three times since the explosion, including stops last Friday and on May 28. He is scheduled to return on Monday.

BP share price rises

BP share prices rose Thursday after a sharp drop the day before. They closed up $3.58, or more than 12 per cent, to $32.78 US on the New York Stock Exchange.

The share price fell 15.8 per cent on Wednesday because of fears that the company would be crippled by spill cleanup and compensation costs.

BP is trying to capture more oil spilling from the well using a containment system that was put in place late last week. As of midnight Thursday, containment operations at the blown-out oil well in the Gulf of Mexico were capturing about 2.5 million litres of oil daily, according to U.S. Coast Guard Admiral Thad Allen. There are almost 159 litres in a barrel.

BP, which had profits of more than $16 billion last year, said Thursday that the cost of the cleanup and containment efforts has hit $1.43 billion.

With files from The Associated Press