(Updates with details in the third paragraph of who will oversee the fund and background from Obama's speech.) By Jared A. Favole Of DOW JONES NEWSWIRES WASHINGTON (Dow Jones)--BP Plc (BP, BP.LN) and the White House have reached a preliminary agreement on a $20 billion fund to help pay for the long-term damages of the Gulf oil disaster that is spewing millions of gallons of oil off the Louisiana coast, according to a person with knowledge of the pact. The preliminary agreement comes as top BP executives are meeting at the White House with President Barack Obama, who on Tuesday in a nationally televised speech accused the company of operating with "recklessness." The fund will be overseen independently by Kenneth Feinberg, who oversaw the historic 9/11 compensation fund in the wake of the Sept. 11, 2001 terrorist attacks, according the person familiar with the preliminary deal. Obama vowed in his speech Tuesday that BP would pay for the disaster, which he characterized as an epidemic that the nation will be "fighting for months and even years." He said he wants BP to create an escrow fund to help pay for future claims for those whose economic livelihoods are threatened or ruined by the catastrophe. Obama said Tuesday he was going to use the meeting Wednesday to tell BP's Chairman Carl-Henric Svanberg that the company needs 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." Obama said the fund will be controlled by a third party, not BP. The meeting with Obama and other administration officials and BP executives comes as the size of the spill was again revised upward, as the latest government figures released Tuesday estimate 35,000 to 60,000 barrels is gushing from the mile-deep well in the Gulf daily. The rate of oil spewing out daily was originally estimated in April at 1,000 barrels and has been updated several times. -By Jared A. Favole, Dow Jones Newswires; 202.862.9256; [email protected] (END) Dow Jones Newswires June 16, 2010 12:53 ET (16:53 GMT)