Brent crude futures climbed $3.11, or 4.3%, to $75.83 a barrel by 0355 GMT, after falling $9.50 on Friday.
U.S. West Texas Intermediate (WTI) crude was up $3.47, or 5.1%, at $71.62 a barrel, having tumbled $10.24 in the previous session.
Oil prices plunged more than 10% on Friday - their biggest one-day drop since April 2020 -- as the new variant spooked investors across financial markets.
There are worries the new variant could derail the global economic recovery, potentially hurting oil demand, while it has also added to concerns that a supply surplus could swell in the first quarter.
"We saw some correction as the Friday's plunge in oil prices has been overdone," said Tatsufumi Okoshi, senior economist at Nomura Securities.
"If the market falls further, OPEC+ may pause the planned increase of crude production to support prices," he said.
The Omicron variant spread around the world on Sunday, with new cases found in the Netherlands, Denmark and Australia even as more countries imposed travel restrictions.
The World Health Organization (WHO) said it was not yet clear whether Omicron, first detected in southern Africa, is more transmissible or dangerous than other variants.
The top U.S. infectious disease official, Dr. Anthony Fauci, told President Joe Biden on Sunday it will take about two weeks to have definitive information on the Omicron.
The Organization of the Petroleum Exporting Countries and its allies (OPEC+) have postponed technical meetings to later this week, giving themselves more time to assess the impact of the Omicron on oil demand and prices, according to OPEC+ sources and documents.
OPEC's joint ministerial monitoring committee was delayed from Tuesday to Thursday. OPEC+ will also meet on Thursday, when a policy decision will likely be announced on whether to adjust its plan to increase output by 400,000 barrels per day in January and beyond.
Some analysts have suggested the group could pause the increases after the release of stocks by oil consuming countries and possible repercussions for demand from new lockdowns to contain the new variant.
"All eyes will be on how the Omicron will affect global economy and fuel demand, OPEC+ action and Iran nuclear talks this week," said Hiroyuki Kikukawa, general manager of research at Nissan Securities.
Talks on reviving the 2015 Iran nuclear deal are to resume in Vienna on Monday, with Iran's atomic advances raising doubt as to whether a breakthrough can be made to bring Tehran and the United States back into full compliance with the accord.