Brent futures increased by $2.71, or 3.2%, to $86.80 a barrel at 0002 GMT, while U.S. West Texas Intermediate (WTI) crude rose $2.26, or 3.4%, to $81.95.
U.S. crude inventories fell by about 3.3 million barrels in the week ended July 24 ,market sources said on Tuesday, citing data from the American Petroleum Institute.
Gasoline inventories, meanwhile, grew by 918,000 barrels, while distillate inventories climbed 355,000 barrels compared with a week earlier, the sources said.
Official inventory data from the Energy Information Administration is due later on Wednesday.
U.S. President Donald Trump, who called off a two-week U.S. bombing campaign over the weekend, told .Fox News on Tuesday that there were "good talks" with Iran, but threatened more strikes if negotiations break down. Iran, however, has denied that it is seeking to resume talks with the U.S.
Meanwhile, a Gulf source and a Western diplomat told Reuters that Oman has presented Iran with a plan to manage the strait, which would include collecting voluntary fees for using the passageway.
The proposals, backed by Gulf states, aim to serve as a basis to end the disruption to trade through the strait caused by the war.
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