Shanghai, Tokyo and Hong Kong advanced. Oil prices gained for a second day.
Wall Street's benchmark S&P 500 index gained 1.2% after the chief White House medical adviser said the omicron variant might be less dangerous. That might allow travel and business restrictions to ease.
Reports from South Africa, where omicron first was spotted, that hospitals haven't been overwhelmed “is fueling some optimism” among traders who sold earlier, said Yeap Jun Rong of IG in a report.
The Nikkei 225 in Tokyo gained 1.3% to 28,282.01 and Hong Kong's Hang Seng advanced 1.4% to 23.678.51. The Shanghai Composite Index added less than 0.1% to 3,589.95.
The Kospi in Seoul advanced less than 0.1% to 2,974.00 and Sydney's S&P-ASX 200 gained 0.4% to 7,273.10.
New Zealand declined while Southeast Asian markets gained.
On Wall Street, the S&P 500 rose to 4,591.67. The Dow Jones Industrial Average rose 1.9% to 35,227.03. The Nasdaq added less than 0.1% to 15,225.15.
More than 85% of stocks in the S&P 500 gained, led by technology and banks.
Airlines, cruise lines and other travel companies that stand to gain from avoiding more anti-coronavirus controls advanced after Dr. Anthony Fauci said early indications suggested omicron may be less dangerous than the earlier delta variant.
Norwegian Cruise Line vaulted 9.5% for the biggest gain in the S&P 500. American Airlines climbed 7.9%, while United Airlines gained 8.3%.
It will still take a few weeks to learn whether omicron is more contagious, causes more severe illness or evades immunity.
Investors also are factoring mixed U.S. jobs data and the Federal Reserve's plan to accelerate its withdrawal of stimulus to cool inflation pressures.
The U.S. government is due to report November consumer inflation on Friday.
In energy markets, benchmark U.S. crude rose 59 cents to $70.08 per barrel in electronic trading on the New York Mercantile Exchange. The contract jumped $3.23 on Monday to $69.49. Brent crude, the price basis for international oils, added 38 cents to $73.46 per barrel in London. It surged $3.20 the previous session to $73.08 per barrel.
The dollar rose to 113.54 yen from Monday's 113.49 yen. The euro advanced to $1.1292 from $1.1278.