Brent crude for November delivery LCOc1 was up 20 cents, or 0.34 percent, at $58.64 a barrel, as of 0418 GMT, Reuters said.
It settled down 1 percent on Tuesday, after earlier hitting $59.49, its highest since July 2015 and more than 34 percent above a 2017 low.
U.S. crude for November delivery CLc1 rose 28 cents, or 0.5 percent, to $52.16, having settled down 0.7 percent after hitting a five-month high of $52.43 in the previous session.
Read alsoReuters: Oil prices mixed as U.S. stockpile rise takes shine off OPEC higher demand viewOil prices have been supported by output curbs of 1.8 million barrels per day by the Organization of Petroleum Exporting Countries (OPEC), and cuts by other major producers, although U.S. crude has lagged behind Brent amid concerns that U.S. production growth could stoke oversupply.
U.S. crude stocks fell by 761,000 barrels last week as refineries boosted production, while gasoline inventories increased and distillate stocks fell, data from industry group American Petroleum Institute showed on Tuesday, in contrast with market expectations.
Refinery crude runs rose by 1.3 million barrels per day, API data showed.
U.S. crude inventories were seen rising for a fourth straight week, an extended Reuters poll showed on Tuesday.
"There's pretty strong upward momentum at the moment," said Ric Spooner, chief market analyst at CMC Markets in Sydney, referring to a better-than-expected near-term supply balance outlook.
Crude oil production in Texas, one of the biggest producers of shale oil in the United States, fell less than 1 percent in July compared with a year ago, the state’s energy regulator said on Tuesday.
"Going forward, oil is likely to remain supported as supply disruptions, combined with solid global demand, will probably continue to lift prices," ANZ said in a research note.
Read alsoReuters: Oil extends gains; Turkey threatens to cut oil flowMonroe Energy, a subsidiary of Delta Air Lines (DAL.N), ran out of crude oil at its 185,000 barrel-per-day Trainer, Pennsylvania, refinery amid shipping delays due to rough seas caused by Hurricanes Jose and Maria, according to a source familiar with the company’s operations and Reuters shipping data.
The U.S. Energy Information Administration (EIA) will release stocks data later in the day.
Turkish President Tayyip Erdogan on Tuesday repeated a threat to cut off the pipeline that carries 500,000-600,000 barrels per day (bpd) of crude from northern Iraq to the Turkish port of Ceyhan.