West Texas Intermediate crude futures were up 6 cents at $57.68 by 0327 GMT, having fallen 3.3% on Tuesday.
Brent crude futures were up 25 cents at $64.60, or 0.4%. They ended down 3.2% in the previous session.
Crude inventories fell by 1.4 million barrels in the week to July 12 to 460 million, industry group the American Petroleum Institute (API) said on Tuesday. That compared with analysts' expectations for a decrease of 2.7 million barrels.
Official data is due out later today from the U.S. government's Energy Information Administration (EIA). If it confirms the fall it will be the fifth consecutive weekly decline, the longest stretch since the beginning of 2018.
"Market participants are looking ahead to the weekly EIA oil inventory data for the U.S., which is expected to show yet another drawdown," Abhishek Kumar, head of analytics at Interfax Energy in London.
"Nevertheless, oil production in the Gulf of Mexico returning to normal following Hurricane Barry will limit price gains," Kumar said.
More than half the daily crude production in the U.S. Gulf of Mexico remained offline on Tuesday in the wake of Hurricane Barry, the U.S. drilling regulator said, as most oil companies were re-staffing facilities to resume production.
The Bureau of Safety and Environmental Enforcement said 1.1 million barrels per day of oil, or 58% of the region's total, and 1.4 billion cubic feet per day of natural gas output remained shut.
The smaller than expected decline in crude stocks suggested production shut-ins caused by Hurricane Barry late last week had little impact on inventories.
Gasoline stocks also fell, declining by 476,000 barrels, compared with analysts' expectations in a Reuters poll for a 925,000-barrel decline.
Distillate fuels stockpiles, which include diesel and heating oil, rose by 6.2 million barrels, compared with expectations for a 613,000-barrel gain, the API data showed.
Oil prices fell on Tuesday after U.S. President Donald Trump said progress has been made with Iran, signaling tensions could ease in the Mideast.
However, Iran later denied it was willing to negotiate over its ballistic missile program, contradicting a claim by U.S. Secretary of State Mike Pompeo, and appearing to undercut Trump's statement.
Tensions between the United States and Iran over Tehran's nuclear program have lent support to oil futures, given the potential for a price spike should the situation deteriorate.
Reuters
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