But BNP's Mr. Tchilinguirian said the oil market may likely "look past" any inventory data until the implications of the U.S.
Front-month London Brent crude for June delivery was up 27 cents, or 0.4 percent, at $68.29, having ended down 10 cents.
The strength of the USA dollar was a headwind for oil, said Bill Baruch, president of Blue Line Futures in Chicago.
The net long position in futures and options tops 600 million barrels of oil, the data shows, meaning that in the event of a sharper drop in price, sellers may find a dearth of buyers.
U.S. West Texas Intermediate crude for May delivery was up 19 cents, or 0.3 percent, at $63.56 a barrel by 0140 GMT after settling down 14 cents.
Global equities sank after China unveiled its charges, which match the scale of proposed US tariffs announced earlier this week and ratchets up tension in a brewing trade war between the world's two largest economies. Trump also tried to quell trade war fears on Wednesday, Tweeting that "We are not in a trade war with China".
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Gasoline stocks fell by 1.1 million barrels, compared with analysts' expectations for a 1.3 million barrels drop.
United States oil inventories shrank the most since January, according to government data on Wednesday, in contrast to a forecast expansion.
US crude inventories fell by 4.6 million barrels last week, compared with analysts' expectations for an increase of 246,000 barrels, EIA data showed on Wednesday.
According to the Weekly Petroleum Status Report, U.S. commercial crude oil inventories, excluding those in the Strategic Petroleum Reserve, of the week ending March 30, decreased by 4.6 million barrels from the previous week.
The extent to which USA production increases counterbalances output cuts from the Organization of the Petroleum Exporting Countries will be critical, said Gene McGillian, manager of market research at Tradition Energy in Stamford.
Lending some price support to oil was a comment on Tuesday by Russian Energy Minister Alexander Novak, referring to earlier comments by Saudi Arabia that talks were taking place on a long-term market co-operation deal between Opec and non-Opec producers led by Russia.