International benchmark Brent futures rose 44 cents to $71.05 a barrels barrel by 10:46 a.m. EDT (1446 GMT). US West Texas Intermediate (WTI) crude oil futures climbed 24 cents to $64.22 a barrel.

US crude stockpiles last week rose to their highest since November 2017 last week as imports increased, while gasoline inventories posted the steepest drawdown since September 2017, the Energy Information Administration said.

Crude inventories swelled by 7 million barrels last week, compared with analysts' expectations for an increase of 2.3 million barrels. Gasoline stocks, however, fell 7.7 million barrels, compared with analysts' expectations in a Reuters poll for a 2 million-barrel drop.

"The report is supportive due to the large gasoline inventory drawn," said John Kilduff, a partner at Again Capital LLC in New York. "Even though the crude oil inventory rise was nearly equal in size, the focus of the complex, as we head into peak summer driving season, is gasoline."

Prices were also boosted by US sanctions on oil exporters Iran and Venezuela, as well as supply cuts by the Organization of the Petroleum Exporting Countries (OPEC) and allies including Russia, a group known as OPEC+.

"With geopolitical risks continuing to impact production from Venezuela and Iran and now also potentially Libya and even Algeria, the crude oil market is likely to remain supported until the price reaches a level that is satisfactory for OPEC and Russia," said Ole Hansen, commodity strategist at Saxo Bank.

An OPEC monthly report released on Wednesday showed that Venezuela's oil output sank last month to a long-term low below 1 million barrels per day (bpd), due to US sanctions and blackouts.  Protests led to the resignation of Algeria's veteran president this month and armed clashes have erupted near the Libyan capital Tripoli, but political upheaval has yet to impact output in major North African producers.

Russia's role in global supply has also came into focus after a senior Russian official signalled that Moscow might seek to raise output, though President Vladimir Putin indicated on Tuesday that current prices suited Russia.

"The Russian camp is increasingly coy about extending supply cuts. Suffice to say this may throw a spanner in the works for a sustained price recovery," said PVM analyst Stephen Brennock.