Stock markets mostly rose worldwide on Tuesday as investors appeared to ride a "Santa Claus rally" that was helped by optimism the Omicron coronavirus variant will not derail the global economic recovery.

Covid-19 cases have surged across the world, prompting governments to impose new measures to limit contagion while the travel industry faced thousands of flight cancelations.

Experts caution against too much optimism around early indications that Omicron causes less severe disease than previous strains, pointing out that it is spreading so fast it could still overwhelm health systems.

But investors seem to be reassured about its effects on the economy.

The US Centers for Disease Control and Prevention helped sentiment on Monday as it cut the isolation period for asymptomatic Covid cases in half to five days.

"That recommendation will reduce some of the pressure of staffing shortages, which in turn is feeding into the market's belief that the economic impact of the Omicron variant is going to be short-lived," said analyst Patrick O'Hare.

Frankfurt's DAX index finished 0.8 percent higher while the Paris CAC 40 closed at a record, rising 0.6 percent to 7,181.11 points. London was closed for a holiday.

On Wall Street, the S&P 500 edged lower, retreating from records, following a mixed session for US stocks in a week of low trading volumes and relatively light news flow.

"You don't have a trend going one way or the other," said Maris Ogg of Tower Bridge Advisors.

Stocks have been on the upswing over the last week as investors bet the latest Covid-19 strain will be less damaging than earlier strains.

Moody's economist Mark Zandi predicted the Omicron wave will dent growth in the first quarter, but "not have a material impact" on 2022 growth overall because a rebound later in the, he said in a note.

"Even after the Omicron wave abates, there will almost surely be others. But we expect each new wave to be less disruptive to the healthcare system and economy than the wave before it," Zandi said.

"An increasingly vaccinated population, booster shots, and new antiviral medications and therapies should help ensure that while many more people will get sick, there will be fewer hospitalizations and deaths."

Stock markets are enjoying a post-Christmas 'Santa Claus rally'
Stock markets are enjoying a post-Christmas 'Santa Claus rally' AFP / Yuki IWAMURA

New York - Dow: UP 0.3 percent at 36,398.21 (close)

New York - S&P 500: DOWN 0.1 percent at 4,786.35 (close)

New York - Nasdaq: DOWN 0.6 percent at 15,781.72 (close)

Frankfurt - DAX: UP 0.8 percent at 15,963.70 (close)

Paris - CAC 40: UP 0.6 percent at 7,181.11 (close)

Tokyo - Nikkei 225: UP 1.4 percent at 29,069.16 (close)

Hong Kong - Hang Seng Index: UP 0.2 percent at 23,280.56 (close)

Shanghai - Composite: UP 0.4 percent at 3,630.11 (close)

London - FTSE 100: FLAT at 7,372.10 points (Friday close)

Euro/dollar: DOWN at $1.1317 from $1.1328 late on Monday

Pound/dollar: DOWN at $1.3428 from $1.3441

Euro/pound: DOWN at 84.21 pence from 84.26 pence

Dollar/yen: DOWN at 114.81 yen from 114.87 yen

West Texas Intermediate: UP 0.5 percent at $75.98 per barrel

Brent North Sea crude: UP 0.4 percent at $78.94 per barrel