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 source 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." Obama vowed in his speech, his first from the Oval Office, 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. The meeting with Obama and other administration officials and BP executives comes as the size of the spill was again revised upward, with the latest government figures released Tuesday estimating 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 12:37 ET (16:37 GMT)