China's factories were struggling to re-open after an extended break and analysts warned that investors might be underestimating the economic damage, but the mood remained strong after another Wall Street surge overnight.
The death toll in mainland China climbed past 1,000 on Tuesday, but the number of new confirmed cases fell.
Zhong Nanshan, an epidemiologist who helped fight the SARS epidemic in 2003, said the situation in some provinces was already improving.
"The peak time may be reached at ... maybe middle or late this month," Zhong told Reuters.
The pan-European STOXX 600 index rose as much as 0.7pc to a record high of 427.46 points.
Basic resources stocks led the gains, rising 1.7pc, as commodity prices recovered from the slowdown in Chinese consumption of raw metals and energy.
"There are some hopes that the peak of virus may be on the horizon, but we are still quite cautious," said TD Securities' European Head of Currency Strategy Ned Rumpeltin. "We are still pretty far from the all clear ... and we just don't know what the macroeconomic impacts are going to be."
In China, factories were slow to reopen after an extended Lunar New Year break, leading analysts at JPMorgan to again downgrade forecasts for growth this quarter.
"The coronavirus outbreak completely changed the dynamics of the Chinese economy," they said in a note.
They assumed the contagion would peak in March and factories would slowly resume opening this month. In that case, growth would slow to around a 1pc annualised pace in the first quarter, before rebounding to 9.3pc in the second.
Should the contagion not peak until April, the economy could contract in the first quarter, with a rebound spread over the second and third quarters, the JPMorgan analysts said.
Even so, MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.9pc, with Shanghai blue chips ahead by 0.8pc.
Japan's Nikkei was closed for a holiday, although Nikkei futures traded up 0.8pc.
FED AHEAD
Markets are now pricing in almost 40 basis points of rate cuts this year by the Federal Reserve to cope with coronavirus damage. The Treasury yield curve slightly inverted to reflect the danger of recession.
Fed Chair Jerome Powell appears before Congress on Tuesday to begin two days of testimony. He's expected to reiterate that the U.S. economy is doing well but that rates can stay low given the current low inflation environment.
The relative outperformance of the U.S. economy is keeping the dollar well-supported, with the euro slipping to a four-month low at $1.0910.
The British pound was last at $1.2906 having touched a two-month trough of $1.2870.
Against a basket of currencies, the dollar was at its highest since mid-October at 98.858 and heading for its sixth day of gains in the last seven against the Japanese yen, which benefits from being a safe haven of its own..
Risk aversion initially helped lift gold to its highest for a week, but the strength of the dollar pulled it back 0.25pc to $1,568.61 per ounce.
Oil prices rose after weeks of decline as traders waited to see how demand in China might fare and whether OPEC could agree to trim supplies.
Brent crude futures gained 64 cents to $53.91 a barrel. U.S. crude rose 50 cents to $50.07.