President Obama sat down with top BP executives at the White House on Wednesday in a highly anticipated meeting that follows repeated administration insistences the company must pick up the tab for the Gulf of Mexico oil disaster.

The meeting between Obama and BP Chairman Carl-Henric Svanberg was also attended by Vice President Joe Biden, Coast Guard Adm. Thad Allen, presidential economic adviser Larry Summers, White House counsel Bob Bauer, domestic policy adviser Melody Barnes and Carol Browner, assistant to the president on energy and climate change.

Also representing BP: company CEO Tony Hayward and Managing Director Bob Dudley, along with BP America CEO Lamar McKay.

The meeting was expected to last roughly two hours, according to a senior administration official.

Referring to the meeting Wednesday, Obama said he would tell Svanberg “that he is to set aside whatever resources are required to compensate the workers and business owners who have been harmed as a result of his company’s recklessness.”

The fund will be controlled not by BP, but by an independent, third party, he said.

In a statement, BP said, “We share the president’s goal of shutting off the well as quickly as possible, cleaning up the oil and mitigating the impact on the people and environment of the Gulf Coast. We look forward to meeting with President Obama … for a constructive discussion about how best to achieve these mutual goals.”

Speedy claims processing was expected to be high on the meeting’s agenda.

David Axelrod, Obama’s senior adviser, has said a new claims plan would call for an independent third party to handle the process, and a White House spokesman said the administration is confident that it has the legal authority to force BP to set up an escrow account for the purpose of paying damages.

BP announced Tuesday that it accelerated commercial large-loss claims and has approved 337 checks for $16 million to businesses that have filed claims in excess of $5,000. Initial payments began over the weekend and will be completed this week, the British energy giant said.

Obama vowed Tuesday to unleash whatever resources may be needed to fight the oil spill in the Gulf of Mexico and to keep the pressure on BP.

“We will fight this spill with everything we’ve got for as long it takes,” Obama said after two consecutive days surveying the Gulf Coast, which is threatened by a massive oil spill that began April 20.

Speaking during prime time from the Oval Office, the president predicted that “in the coming days and weeks,” efforts to contain the leak “should capture up to 90 percent of the oil leaking out of the well.”

Ending the leak should occur later in the summer, when a relief well being drilled by BP is slated for completion, he said.

During his speech, Obama made no reference to the announcement earlier Tuesday by government scientists they had increased their estimate of oil flowing into the Gulf of Mexico by 50 percent — to between 35,000 and 60,000 barrels per day.

That translates into 1.5 million gallons to 2.5 million gallons per day.

The government’s previous estimate, issued last week, was 20,000 to 40,000 barrels per day.

(Read More: CNN)