West Texas Intermediate crude futures were up 31 cents at $57.93 a barrel by 0829 GMT.
Brent crude futures gained 53 cents to $64.88 a barrel. Both benchmarks had shed more than 3% on Tuesday.
Crude inventories fell by 1.4 million barrels in the week to July 12 to 460 million barrels, the American Petroleum Institute (API) said on Tuesday. That compared with analyst expectations for a drop of 2.7 million.
The smaller-than-expected decline suggested production shut-ins caused by Hurricane Barry late last week had little impact on inventories.
Gasoline stocks also fell, the API data showed, but less than expected, and distillate inventories rose more than forecast.
Official data from the U.S. government's Energy Information Administration (EIA) is due at 1430 GMT. If confirmed, it would be the fifth consecutive weekly decline, the longest stretch since the beginning of 2018.
More than half of daily crude production in the 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.
Oil prices slumped on Tuesday on increased hopes for a return of Iranian crude to the global oil market after U.S. President Donald Trump said progress had been made with Tehran, signalling tensions could ease in the Middle East.
However, Iran later denied it was willing to negotiate over its ballistic missile programme, contradicting a claim by U.S. Secretary of State Mike Pompeo, and appearing to undercut Trump's statement.
"It is hard to believe that either the United States or the Iranian stance would change drastically, therefore yesterday's sell-off might turn out to be an excellent buying opportunity," PVM analysts wrote.
"Especially if this afternoon's EIA (U.S. crude) stock data will be more constructive than last night's API report."