U.S. West Texas Intermediate (WTI) crude futures rose 21 cents, or 0.3%, to $65.49 a barrel at 0013 GMT, adding to a 36 cent rise on Tuesday.
Brent crude futures climbed 15 cents, or 0.2%, to $68.70 a barrel, adding to a 23 cent gain on Tuesday.
"Crude oil gained as investors continue to bet on a bright outlook for demand. A weak U.S. dollar also lent support," ANZ Research said in a note.
Data from the American Petroleum Institute industry group showed U.S. crude oil stocks fell by 2.5 million barrels in the week to May 7, according to two market sources.
The drop was slightly less than expected. Eight analysts polled by Reuters had estimated, on average, that crude stocks fell by 2.8 million barrels.
The drawdown came before the Colonial Pipeline was hit by a cyberattack last Friday which forced the pipeline, which transports more than 2.5 million barrels a day of fuel, to shut down. The operator said it hopes to restart a large portion of the network by the end of the week.
In the meantime, the market remained on edge, as gasoline stations from Florida to Virginia began running out of fuel on Tuesday as drivers rushed to top up their tanks and pump prices rocketed.
U.S. unleaded gasoline prices hit an average $2.99 a gallon, the highest since November 2014, the American Automobile Association said.
Oil prices were also supported by the latest outlook from the Organization of the Petroleum Exporting Countries (OPEC), which stuck to a forecast for a strong recovery in world oil demand in 2021 with growth in China and the United States outweighing the impact of the coronavirus crisis in India.
OPEC said it expects demand to rise by 5.95 million bpd this year, unchanged from its forecast last month. However, it cut its demand outlook for the second quarter by 300,000 bpd due to soaring COVID-19 infections in India.
"India is currently facing severe COVID-19-related challenges and will therefore face a negative impact on its recovery in the second quarter, but it is expected to continue improving its momentum again in the second half of 2021," OPEC said in its monthly report.
