U.S. West Texas Intermediate crude futures fell 63 cents, or 0.9%, to $73.16 a barrel by 0510 GMT. The contract did not trade on Friday because U.S. markets were closed for the Christmas holiday.
Brent crude rose 20 cents, or 0.3%, to $76.34 a barrel after settling down 0.92% on Friday.
Both contracts jumped 3% to 4% last week after early data suggested that the Omicron variant of COVID-19 may cause a milder level of illness.
However, the highly transmissible variant is causing COVID-19 case numbers to surge across the world.
In the past three days, thousands of passengers travelling during Christmas have been stranded after U.S. airlines cancelled flights due to COVID-related staffing shortages.
"Lower travel equalling lower economic activity in the U.S. equals lower WTI, the U.S. oil benchmark," said OANDA analyst Jeffrey Halley said.
Oil markets, in general, remain cautious about near-term demand, market watchers said.
"Though Omicron is spreading faster than any COVID-19 variant yet, a relatively relieving (piece of) news is that most people infected with Omicron are showing mild symptoms, as least so far," said Leona Liu, analyst at Singapore-based DailyFX.
"That said, oil prices did suffer for the Omicron concerns, but the downside pressure may ease if the variant is proved to be more mild," she added.
In Europe, natural gas prices touched record highs last week on tight supplies, supporting Brent crude prices.
Russian President Vladimir Putin said on Friday that the European Union can only blame its own policies for record gas prices, saying some of its members resell cheap Russian gas at much higher prices within the bloc.
Looking ahead, oil investors are focused on the next OPEC+ meeting on Jan. 4.
The Organization of the Petroleum Exporting Countries (OPEC and allies including Russia, known as OPEC+, will meet to decide whether to go ahead with a 400,000 barrels per day (bpd) production increase in February.
Russia believes oil prices are unlikely to change significantly next year with demand recovering to pre-pandemic levels only by the end of 2022, Deputy Prime Minister Alexander Novak said on Friday.
