US West Texas Intermediate (WTI) crude futures jumped 33 cents, or 0.5%, to $73.18 a barrel at 0217 GMT, after falling 60 cents on Tuesday.
Brent crude futures jumped 42 cents, or 0.6%, to $75.23 a barrel, after giving up 9 cents on Tuesday.
The American Petroleum Institute industry group reported crude stocks fell by 7.2 million barrels for the week ended June 18, according to two market sources.
That was a much bigger drawdown than the 3.9 million barrels which nine analysts polled by Reuters had expected on average.
If official figures from the US Energy Information Administration due later on Wednesday confirm the drawdown, it would be the fifth straight week of declines, showing the US market tightening, ING Economics said in a note.
All eyes are on what the Organization of the Petroleum Exporting Countries and allies, together known as OPEC+, plan to do when they meet on July 1 as they gauge the demand recovery.
OPEC+ is discussing a gradual increase in supply from August, but no decision has been made yet on the exact volumes, two OPEC+ sources said on Tuesday.
“The producer group once again faces some tough decisions as the market continues to show tightness. Global progress in COVID-19 vaccination campaigns have seen consumer mobility across US, China and Europe recover sharply,” ANZ commodity analysts said in a note.
“However the prospect of Iranian oil hitting the market in the near term has seen OPEC remain cautious about increasing supply,” they said.
A retreat in the US dollar from a two-month high hit late last week has also helped prop up oil prices, as a weaker greenback makes oil less expensive in other currencies.
