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CORRECTED-UPDATE 3-Oil futures rise on U.S. stockpile draw, doubts over climate accord

climate accord@ (Corrects Brent contract to August, not July)

* Trump could pull out of climate accord

* That would boost outlook for fossil fuels -analyst

* U.S. stockpile drawdown helps support oil prices

TOKYO, June 1 (Reuters) - Oil futures rose on Thursday from a three-week low touched the previous session, buoyed by expectations the United States could pull out of a global climate accord and by a report that showed U.S. crude stockpiles had fallen more than expected.

Trump said he would announce later on Thursday a decision on whether to keep the United States in a global pact to fight climate change, as a source close to the matter said he was preparing to pull out of the Paris agreement.

"If he actually withdraws the U.S from the climate accord, this would signal his intention to further roll-back emission regulations that would favor the use and demand of fossil fuels, thus giving a much needed boost to oil prices," said Jonathan Chan, investment analyst at Phillip Futures in Singapore.

Brent crude futures for August were up 58 cents, or 0.8 percent, at $51.34 a barrel by 0739 GMT, after trading higher earlier.

On Wednesday, they fell $1.53, or 3 percent, to settle at $50.31 a barrel. It was Brent's lowest close since May 10 and the contract dropped 2.7 percent last month, the third monthly decline.

U.S. West Texas Intermediate crude futures were up 64 cents, or 0.8 percent, at $48.96 a barrel.

They dropped $1.34, or 2.7 percent, in the previous session to settle at $48.32 per barrel, the lowest close since May 12. The U.S. benchmark also fell for a third month in May, declining 2 percent.

Data from the American Petroleum Institute (API) showed crude inventories were down by 8.7 million barrels at 513.2 million in the week to May 26. That compared with analyst expectations for a decrease of 2.5 million barrels.

The U.S. Energy Information Administration (EIA) report on stockpiles is due at 11:00 a.m. EDT (1500 GMT) on Thursday, delayed by a day because of the Memorial Day holiday on Monday.

Further gains may be limited for the two major oil benchmarks as bearish news keeps coming from the Organization of the Petroleum Exporting Countries (OPEC) and other producers including Russia that are locked in a battle against rising shale production in their efforts to boost prices.

Oil futures have given up all the gains posted in advance of last week's agreement between OPEC and non-OPEC producers to extend a production cut for a further nine months.

Output from OPEC rose in May, the first monthly increase this year, a Reuters survey found.

Higher supply from Nigeria and Libya, OPEC members that are exempt from the production-cutting deal, offset improved compliance by others.

(Reporting by Aaron Sheldrick; Editing by Joseph Radford and Biju Dwarakanath)