The benchmark German 10-year Bund yield was last up nearly 2 bps at -0.42pc, but remained within sight of the -0.45pc lows hit on Monday.
Other euro zone government bond yields were also around 2 bps higher, whilst U.S. 10-year Treasury yields outperformed, rising by 5 bps to 1.57pc.
The death toll from coronavirus, which has infected over 20,000 people globally, more than twice as many as the 2002/2003 SARS outbreak that also originated in China, now stands at 427.
Hong Kong reported its first death on Tuesday, the second outside mainland China.
Chinese authorities have stepped up measures to relieve pressure on the economy and reassure international investors.
The central bank, the People's Bank of China (PBOC), will inject 500 billion yuan ($71.50 billion) through open market operations on Tuesday, traders said, after an injection of 1.2 trillion yuan a day earlier.
It also set its official yuan midpoint at the lowest level in over one month.
Policy sources said PBOC is likely to lower its key lending rate on Feb. 20, and cut banks' reserve requirement ratios soon, while the Chinese government could lower the planned 2020 economic growth target of around 6 percent.
Bank of Japan Governor Haruhiko Kuroda said on Tuesday the economic impact of the new coronavirus was a concern and he would pay "maximum attention" to its effect on Japan's economy and prices.
Some bond market analysts said the latest figures suggested the spread of the virus might be slowing, although health authorities have not said that.
"The reason this is important is that at the time of SARS, this proportionately moderating statistic is the one which highlighted the peak of fears and bottom of the market in regards to virus concerns," said Chris Bailey, European strategist at Raymond James.
The World Health Organization (WHO) has declared the flu-like virus a global emergency and experts say much is still unknown about the pathogen, including its mortality rate and transmission routes.
Chinese data suggesting the virus is less deadly than the 2002-03 SARS outbreak, although it appears to spread much faster, also offered investors some comfort.
Andy Cossor, rates strategist at DZ Bank, said a fall in oil prices, which is likely to curb inflation growth, had also helped foster "a slightly smaller appetite for safe havens," such as government bonds.
Brent crude sank to a more than one-year low of $53.95 a barrel on Tuesday.
European yields are likely to rise further as countries across Europe line up to issue new debt, ING analysts said.
"We estimate net EGB supply will amount to 52 billion euros ($57.49 billion) in February, compared to 56 billion euro last month," they wrote in a note to clients.