U.S. West Texas Intermediate (WTI) crude futures rose 48 cents, or 0.7%, to $66.17 a barrel at 0440 GMT, after climbing to $66.58, a level not seen since March 8.
Brent crude futures were up 49 cents, or 0.7%, at $69.37 barrel after touching a more than seven-week high of $69.78 earlier in the session.
Both benchmark contracts rose nearly 2% on Tuesday ahead of data from the American Petroleum Institute (API) industry group.
"Crude oil prices appear to be supported by a large draw in crude and gasoline inventories, according to API figures," said Margaret Yang, a strategist at Singapore-based DailyFX.
"The energy demand outlook is brightened by eased lockdown measures in parts of the U.S. and UK, which helped to offset concerns over lower demand from India and Japan. The upcoming summer driving season may further boost fuel demand and support oil prices."
API figures showed crude stocks fell by 7.7 million barrels in the week ended April 30, according to two market sources. That was more than triple the drawdown expected by analysts polled by Reuters.
Traders are awaiting data from the U.S. Energy Information Administration due at 10:30 a.m. EDT (1430 GMT) on Wednesday to see if official data shows such a large drawdown.
"If confirmed by the EIA, that would mark the largest weekly fall in the official data since late January," Commonwealth Bank analyst Vivek Dhar said in a note.
The rise in oil prices to nearly two-month highs has been supported by COVID-19 vaccine rollouts in the United States and Europe, paving the way for pandemic lockdowns to be lifted and air travel to pick up.
So far that has more than offset a drop in fuel demand in India, which is battling a surge in infections.
"However, if we were to eventually see a national lockdown imposed, this would likely hit sentiment," ING Economics analysts said of the situation in India.
