MSCI's broadest index of Asia-Pacific shares outside Japan rose 1.0%, led by gains in South Korea and Australia. Japan's Nikkei inched up 0.1%.
"Given the extent of the shutdowns in China as well as the rapid rise in the virus that is likely to continue through March or April, a significant hit to China and regional growth is very likely," said JPMorgan economist Joseph Lupton.
"We would assume that in addition to bridging any funding stresses, fiscal policies will need to be ramped up to support growth once the contagion gets under control."
The Shanghai Composite stood flat in choppy early trading, while the blue-chip CSI300 rebounded 0.9%, one day after an almost 8% slide on Monday as markets resumed from the Lunar New Year holiday. Hong Kong's Hang Seng advanced 0.7%.
"Chinese authorities have been providing a lot of support for the financial markets. There's a level of assurance that the rout would not be allowed to go on much further than necessary," Christy Tan, head of markets strategy for Asia at National Australia Bank in Singapore.
"This could prove to be temporary if we see worse news or little sign of reaching containment of the (coronavirus) situation," she added.
In an effort to stop the rout, China's state-backed Securities Times published an op-ed on Tuesday to call on investors not to panic.
That followed moves by China's securities regulator on Monday to limit short selling and stop mutual fund managers selling shares unless they face investor redemptions, according to Reuters.
E-Mini futures for the S&P 500 gained 0.3%, extending a 0.7% bounce overnight, even after disappointing earnings results from Alphabet Inc.
Wall Street had taken comfort in a surprisingly solid reading of U.S. manufacturing and the Dow ended Monday with a rise of 0.5%, while the S&P 500 gained 0.7% and the Nasdaq 1.3%.
"This is just a typical reversal after a big fall. Vague concerns about Wuhan virus are still weighing on U.S. stocks," said Masanari Takada, cross asset strategist at Nomura Securities in Tokyo.
Factory activity rebounded in January after contracting for five straight months amid a surge in new orders.
The ISM index rose to 50.9, the highest since July, from an upwardly revised 47.8, though the survey was taken before the virus spread in earnest.
The upbeat report nudged Treasury yields up from deep lows and gave the U.S. dollar a modest lift.
In early Asian trade, oil futures staged a modest rebound, one day after slumping to the lowest in more than a year as the coronavirus outbreak curtailed Chinese demand.
Brent crude added 0.5% to $54.73 a barrel, while U.S. crude gained 0.7% to $50.44.
A swath of commodities from copper to iron ore joined oil in the dumpster amid fears the drag on Chinese industry and travel would sharply curb demand for fuel and resources.
The Dalian Commodity Exchange's most-traded iron ore futures contract, expiring in May, tumbling more than 5% in early trade.
In the currency market, the dollar firmed to 108.66 yen , from an overnight low of 108.30, while the euro faded a fraction to $1.1059 but remained well within recent snug ranges.
Against a basket of currencies, the dollar bounced back to 97.837 from a trough of 97.406.
Sterling was nursing its wounds at $1.2987 having shed 1.6% overnight when the UK government laid out a tough opening stance for future trade talks with the European Union following its departure from the bloc last week.
The fall erased all the gains made after the Bank of England's decision last week to keep interest rates on hold.
Spot gold was off at $1,576.34 per ounce, from a top of $1.591.46, as the dollar firmed and safe haven demand waned a little.
(Additional reporting by Noah Sin; Editing by Sam Holmes)
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