The MSCI world equity index, which tracks shares in 50 countries, was up 0.2% - its highest since Nov. 26, when Omicron fears first hit markets.
"Every day that passes without a wave of severe cases driven by Omicron is offering more hope that this won't be the curveball to throw the recovery off course," wrote Deutsche Bank strategist Jim Reid in a note to clients.
Markets cheered news that BioNTech and Pfizer said that a three-shot course of their COVID-19 vaccine was shown to generate a neutralising effect against the new Omicron variant in a laboratory test.
"Clearly in the very short term uncertainty has risen over the Omicron virus... but overall at this stage we do not believe it will derail the macro picture in the medium-term," said Jeremy Gatto, multi-asset portfolio manager at Unigestion.
London's FTSE 100 and the British pound were knocked by reports that Britain could implement tougher COVID-19 measures as early as Thursday
But by 1159 GMT, the FTSE 100 had partly recovered its losses and was up 0.3% on the day .
U.S. stock futures pointed to a higher open for Wall Street, with S&P 500 e-minis up 0.5% , having jumped after the updated from Pfizer.
OUTLOOK FOR RATES
Oil prices eased as investors waited for more information about the extent to which the variant would impact demand.
The dollar index was steady around 96.291 , while the euro was up 0.1% at $1.1275.
The euro-dollar pair has struggled to recover from the 2021 lows it reached in November, hurt by expectations that the U.S. Federal Reserve will tighten monetary policy more quickly than the dovish European Central Bank.
Last week, Fed Chair Jerome Powell said it might be time to stop seeing inflation as transitory, suggesting the central bank could speed up tapering.
"The market is pricing between two to three hikes next year now. We think that that pricing is too optimistic. We believe that the Fed will actually be slower to deliver on these rate hikes," said Unigestion's Gatto, adding that this would be supportive for equities.
The U.S. 10-year Treasury yield, which had its biggest weekly drop since June 2020 last week due to a combination of Powell's hawkish comments and fears over Omicron, was steady at 1.4717%.
U.S. inflation data is due on Friday.
Meanwhile, shares in China's Evergrande Group hit a record low, after a missed debt payment deadline put the developer at risk of becoming the country's biggest defaulter - but the news had limited global market impact because it is already "well-priced" by the market, Unigestion's Gatto said.
In virtual talks, President Joe Biden warned Russian President Vladimir Putin that the West would impose "strong economic and other measures" on Russia if it invaded Ukraine, while Putin demanded guarantees that NATO would not expand farther eastward.
(Reporting by Elizabeth Howcroft; Editing by Alex Richardson, William Maclean) ((Elizabeth.Howcroft@thomsonreuters.com; +44 02075427104;))