Brent crude oil futures rose by 17 cents, or 0.3%, to $69.13 a barrel by 0343 GMT, and U.S. West Texas Intermediate (WTI) crude futures gained by 8 cents, or 0.1%, to $65.71 a barrel.
Both benchmarks had hit their highest since mid-March on Wednesday before retreating.
"As the roll-out of vaccines continues and a pent-up summer driving season continues to manifest, this trend should accelerate, keeping demand for motor fuels robust and boosting market confidence in the recovery story," analysts from Citi Group said in a note.
U.S. crude stocks fell more than expected last week as refining output rose and exports surged, the Energy Information Administration said on Wednesday.
Crude inventories fell by 8 million barrels in the week to April 30 to 485.1 million barrels, compared with expectations in a Reuters poll for a 2.3 million-barrel drop.
U.S. gasoline stocks rose by 737,000 barrels in the week, the EIA said, against a forecast for a 652,000-barrel draw.
"We think U.S. demand is strong," said analysts from Commonwealth Bank of Australia. "The U.S. refinery utilisation rate is now above the five-year average."
The Commonwealth Bank analysts said U.S. jet fuel demand is expected to surge by 30% in the second quarter compared with the first quarter on increased domestic travel.
Pandemic-related restrictions in the United States and parts of Europe are easing, but infections are still on the rise in major crude oil importers India and Japan, capping price gains.
Meanwhile, militants using bombs attacked two oil wells at an oilfield close to the northern Iraqi city of Kirkuk on Wednesday, killing at least one policeman and setting off fires, the country's oil ministry said. read more
Industry sources said the attack had not affected output. An oil ministry statement did not comment on production.
