U.S. West Texas Intermediate (WTI) crude futures fell 17 cents, or 0.2%, to $72.21 a barrel at 0155 GMT.
Brent crude futures fell 11 cents, or 0.2%, to $74.91 a barrel.
"Look at what's happening with Omicron - that's a negative which people are trying to digest. Are we going to be in line for some new restrictions? That's what the market's trying digest," said Commonwealth Bank commodities analyst Vivek Dhar.
In Denmark, South Africa and the United Kingdom, the number of new Omicron cases has been doubling every two days. Denmark's Prime Minister Mette Frederiksen on Thursday warned the government may impose further curbs to limit the spread of Omicron.
In the United States, the rapid spread of the Omicron variant has led some companies to pause plans to get workers back into offices.
"Crude continues to face significant headwinds from the Omicron variant, with the demand outlook for early next year taking a hit, but OPEC+ stands ready to act should the situation necessitate which will continue to backstop prices for now," OANDA analyst Craig Erlam said in a note.
The Organization of the Petroleum Exporting Countries, Russia and allies, together known as OPEC+, have said they could meet ahead of their scheduled Jan. 4 meeting if changes in the demand outlook warrant a review of their plan to add 400,000 barrels per day of supply in January.
Benchmark Brent and WTI both gained around 2% on Thursday, buoyed by record U.S. implied demand and a weaker U.S. dollar as the Bank of England surprised markets with a rate hike, taking a more hawkish stance than the Federal Reserve.
WTI was poised to finish the week up 0.7% while Brent was headed for a 0.4% loss for the week.
