U.S. West Texas Intermediate (WTI) crude futures gained 35 cents, or 0.5%, to $73.11 a barrel at 0244 GMT after jumping 2.3% in the previous session.
Brent crude futures climbed 40 cents, or 0.5%, to $75.69 a barrel, extending a 1.8% gain in the previous session.
The big gains on Wednesday were partly spurred by a larger-than-expected drawdown in U.S. crude stockpiles last week.
A weaker U.S. dollar buoys oil markets as it makes commodities cheaper for those holding other currencies. The dollar fell to near a one-week low after data on Wednesday showed U.S. consumer confidence improving more than expected in December.
Oil's climb has come even as governments reimposed a range of restrictions to slow the spread of Omicron. The Chinese city of Xian on Wednesday ordered its 13 million residents to stay home, while Scotland imposed gathering limits from Dec. 26 for up to three weeks, and two Australian states reimposed mask mandates as cases surged.
The market has shrugged off the potential impact of mobility restrictions on fuel demand because the Organization of the Petroleum Exporting Countries (OPEC), Russia and allies, together called OPEC+, has left the door open to reviewing their plan to add 400,000 barrels per day of supply in January.
"The Omicron variant could still lead to more restrictive measures across Europe and Asia, but prices won't break since OPEC+ can easily adjust their production levels," said OANDA analyst Edward Moya in a note.
