Kuwait, Bahrain, Oman, Afghanistan and Iraq reported their first cases, while South Korea, which has the most virus cases outside China, said it aims to test more than 200,000 members of a church at the centre of a surge in the infections.
"I don't think this (rise in markets) has got any longevity," said Jeffrey Halley, senior market analyst at OANDA.
"It's what I call a dead cat bounce... that I think will run out of steam very quickly against the bigger global backdrop."
Indonesia was an exception, with the benchmark index closing at its lowest in over 15 months weighed down by losses in the consumer and resources sector.
Chemicals maker Chandra Asri Petrochemical fell 9.5%, while cigarette maker Hanjaya Mandala Sampoerna dropped 2.4%.
Malaysian shares, which closed at an over eight-year low on Monday amid political turmoil, ended 0.7% higher, helped by gains in the banking and healthcare sectors.
Lender Malayan Banking rose 1% and hospitals operator IHH Healthcare gained 1.6%.
Singapore stocks snapped three straight sessions of losses, helped by gains in benchmark heavyweights Oversea-Chinese Banking Corp and Capitaland Ltd.
Thai stocks ended slightly higher, recovering from an over three-year low hit earlier in the session.
"The Thai market is very volatile today, with news from external fronts being followed. Going ahead, I think a lot depends on the developments in the COVID-19 outbreak," said Teerada Charnyingyong, an analyst with Phillip Capital Thailand.
The Philippine bourse was closed on account of a public holiday.
By Soumyajit Saha
