Safe-harbour government bonds went the other way with yields - which move inverse to bond prices - up 2.5% on Germany's benchmark 10-year Bund after falling to a three-month low on Monday.
Reports in South Africa said Omicron cases there had only shown mild symptoms and the top U.S. infectious disease official, Anthony Fauci, told CNN "it does not look like there's a great degree of severity" so far.
"Good news relating to the severity of Omicron should be taken with a pinch of salt. Faster transmission could offset the benefits of milder symptoms," researchers at ING said in a note. "More broadly, it is still early days, even if markets are starting to display Omicron fatigue."
The gains also came after China's central bank on Monday injected its second shot of stimulus since July by cutting the amount of cash that banks must hold in reserve.
There was still uncertainty about its property sector as Evergrande teetered on the brink of default again but data showing much stronger import growth was "a positive sign on the strength of domestic demand", RBC analyst Adam Cole said.
Elsewhere, Australia's S&P/ASX200 rose 0.95%, while Japan's Nikkei advanced 2.1% as risk-on sentiment pushed markets higher.
MSCI's main Asia ex-Japan benchmark has lost about 5% so far this year, with Hong Kong markets figuring among the big losers, while Indian and Taiwan stocks outperformed.
Shares in embattled developer Evergrande edged up 1.7% after hitting a record low on Monday as markets waited to see if the real estate giant has paid $82.5 million with a 30-day grace period coming to an end.
Elsewhere, markets were supported by gains on Wall Street, where economically sensitive stocks outperformed.
"While epidemiologists have rightly warned against premature conclusions on Omicron, markets arguably surmised that last week's brutal sell-off ought to have been milder," Vishnu Varathan, head of economics and strategy at Mizuho Bank, said in a note.
"After all, early assessments of Omicron cases have been declared mild, spurring half-full relief."
Also supporting the dollar in FX markets was the expectation the Federal Reserve will accelerate the tapering of its bond-buying programme when it meets next week in response to a tightening labour market.
Oil prices jumped another 2% to $74.60 a barrel, adding to a near 5% rebound the day before as concerns about the impact of Omicron on global fuel demand eased.
Copper prices also ticked higher while gold was steady at $1,778.5 per ounce on expectations U.S. consumer price data due later this week will show inflation quickening.
(Additional reporting by Anshuman Daga in Singapore; Editing by Nick Macfie) ((email@example.com; +44 (0)20 7513 4042; Reuters Messaging: firstname.lastname@example.org Twitter @marcjonesrtrs))