Brent crude futures were up 11 cents, or 0.2 percent, to $62.25 a barrel by 11:14 a.m. EDT (1514 GMT).

US West Texas Intermediate crude futures rose 5 cents, or 0.1 percent, to $53.95 a barrel. On Tuesday, it had recorded its biggest daily rise since early January.

After weeks of swelling, US crude stocks fell by 3.1 million barrels in the last week compared with analysts' expectations for a draw of 1.1 million barrels, the Energy Information Administration said.

"Definitely what we saw here is more of a normal report for this type of year," said Phil Flynn, analyst at Price Futures Group in Chicago. "Even with the bullish report, after the big run-up yesterday, the market is hesitant to drive a lot higher."

Comments by US President Donald Trump that preparations were starting for him to meet Chinese President Xi Jinping next week at the G20 summit in Osaka, Japan, also helped oil prices.

Trump has repeatedly threatened to slap more tariffs on Chinese goods.

Tensions remain high in the Middle East after last week's tanker attacks. Fears of a confrontation between Iran and the United States have mounted, with Washington blaming Tehran, which has denied any role.

Trump said he was prepared to take military action to stop Iran having a nuclear bomb but left open whether he would approve the use of force to protect Gulf oil supplies.

On Wednesday, oil markets shrugged off a rocket attack on a site in southern Iraq used by foreign oil companies.

"It is interesting to note that the crude oil futures market could not rally on hawks planting bombs in the Strait of Hormuz but could rally on doves planting quantitative easing," Petromatrix's Olivier Jakob said in a note.

"This is an oil market that doesn't know how to react when an oil tanker blows up but knows how to react when the head of a central bank makes some noise."

The US Federal Reserve concludes its latest two-day policy meeting on Wednesday and is expected to leave interest rates on hold but flag whether it plans to cut rates later this year.

The Fed may nod to recent weaker-than-expected jobs numbers and softer inflation, and drop from its policy statement a pledge to be "patient" before changing rates.

Members of the Organization of the Petroleum Exporting Countries have agreed to meet on July 1, followed by a meeting with non-OPEC allies on July 2, after weeks of wrangling over dates.

OPEC and its allies will discuss whether to extend a deal on cutting 1.2 million barrels per day of production that runs out this month.