Industry data from the American Petroleum Institute showed on Tuesday that USA crude inventories fell by 2 million barrels last week, compared with analysts' expectations for a draw of 1.8 million barrels.
"This is occurring because of the rapid increase in production from USA shale coupled with the tightening of supplies elsewhere through the actions of Opec and Russian Federation", said William O'Loughlin, investment analyst at Australia's Rivkin Securities.
Brent crude futures added 25 cents, or 0.33 percent, to $75.53 a barrel by 0717 GMT, after settling down 2 percent at $75.29 on Monday.
The price of oil has been under pressure given the potential for a trade war escalating over Washington's pursuit of tariffs. Crude, the global benchmark, was mostly unchanged.
Opec and Russian Federation meet on 22 June to discuss production policy.
OPEC will meet on June 22 and needs a consensus of all members to officially change its output policy.
USA crude oil production broke a record last week at 10.47 million barrels per day.
Further weighing on prices has been rising US output, which hit another record last week at 10.8 million bpd. Once again, the nemesis of an oil bull run is higher out in the United States and some non-Opec producers like Mexico, Columbia and Azerbaijan.
Trump announced last month that the US would back out of a deal with Iran that sought to curb the country's nuclear ambitions in exchange for sanctions relief.
"OPEC will not bow and obey" to USA pressure to increase oil production, said Hossein Kazempour Ardebili, one of Iran's representatives to the organization.
But many European companies are already severing ties with Tehran for fear of facing secondary sanctions from the United States, which could mean losing access to the USA dollar clearing system.
Saudi Arabia, the world's largest oil exporter, raised pricing on key crude grades for buyers in Asia to the highest since 2014 as demand builds in the country's biggest market amid threats to rival suppliers. As speculation swirls over whether Opec and its allies will relax the caps at a meeting in Vienna later this month, Goldman Sachs Group Inc is still bullish on oil as it says stockpiles will continue to diminish this year.