Europe's main stock markets were up 0.5 percent a day after slumping around 2.5 percent.
Tokyo extended its losses but Tuesday's drop was less sharp at 0.6 percent.
Dollar falls against safehavens such as the yen and Swiss franc were also less sharp, while oil prices recovered.
"Calm has descended across global markets after yesterday's sell-off," said Neil Wilson, chief market analyst at Markets.com.
Markets remain "open to further falls if it becomes clear that infection is spreading more rapidly, but for now equity markets are entering a process of stabilisation", he added.
China on Tuesday urged its citizens to postpone foreign travel to curb a viral outbreak that has killed 106 people, as the first cases of human-to-human contagion were detected abroad.
While traders have sought safety, for example buying into gold, oil tanked Monday on expectations that demand in China, the world's top consumer, will be hammered.
The outbreak comes during the Lunar New Year break when hundreds of millions of people criss-cross China and spend huge amounts of money.
Analysts said there were growing fears the crisis could become as bad as the SARS outbreak that rocked markets and the global economy 17 years ago.
The VIX "fear" index, which measures market volatility, soared by one quarter Monday to the highest level since October, when investors were worried about China-US trade talks.
The crisis comes just as the world economy was showing signs of stability after a long-running growth slowdown.
"Given that China has rapidly increased its role in the global supply chains, the market continues to price in the worst case, negative growth shock scenarios," said AxiCorp's Stephen Innes.
"For the most part, traders are flying blind, knowing nothing about the actual implications of (the virus) for global growth," he said, adding "there remains a growing sense in the market that contagion levels could get worse before they get better".
London - FTSE 100: UP 0.5 percent at 7,449.25 points
Frankfurt - DAX 30: UP 0.4 percent at 13,254.52
Paris - CAC 40: UP 0.5 percent at 5,893.19
EURO STOXX 50: UP 0.5 percent at 3,695.99
Tokyo - Nikkei 225: DOWN 0.6 percent at 23,215.71 (close)
Seoul - Kospi: DOWN 3.1 percent at 2,175.77 (close)
Hong Kong - Hang Seng: Closed for a public holiday
Shanghai - Composite: Closed for a public holiday
New York - DOW: DOWN 1.6 percent at 28,535.80 (close)
Dollar/yen: UP at 109.06 yen from 108.90 yen at 2200 GMT
Euro/dollar: DOWN at $1.1009 from $1.1019
Pound/dollar: DOWN at $1.3015 from $1.3057
Euro/pound: UP at 84.58 pence from 84.39 pence
Brent Crude: UP 0.2 percent at $59.45 per barrel
West Texas Intermediate: UP 0.5 percent at $53.39