The market futures markets are indicating a rise of 0.5 percent when Wall Street opens for business.
China's Shanghai Composite tumbled 8.7 percent, then rebounded slightly as Chinese regulators moved to stabilize markets reopening from a prolonged national holiday despite a rising death toll from the coronavirus has spread to more than 20 countries.
The Shanghai benchmark ended the day 7.7 percent lower, wiping some $393 billion from China's benchmark stock index, accoridng to Reuters.
Japan's Nikkei lost 1.1 percent and Hong Kong's Hang Seng climbed 0.2 percent.
In Europe, London's FTSE added 0.5 percent, Germany's DAX gained 0.2 percent and France's CAC rose 0.3 percent.
Airlines have cancelled hundreds of flights and cities in China have imposed stronger limits on public activities in moves that have led economists to begin downgrading their growth estimates for this year.
Many analysts have dropped their growth estimates for China, the world's second-largest economy, to near 5 percent from earlier forecasts of 6 percent growth for the year.
With tens of millions of Chinese living in cities ordered to mostly stay home, retailer and tourism-related businesses already are suffering.
The number of people infected by the virus first found in the central Chinese city of Wuhan had risen above 17,000 as of Sunday night, the government said. It has killed more than 360 people, all but one in China.
China's central bank announced plans Sunday to inject 1.2 trillion yuan ($173 billion) into the markets to cushion the shock from the outbreak of a new virus when trading resumed.
The Lunar New Year holiday, usually a week long, had been prolonged by three days as a precaution.
On Wall Street on Friday, the Dow skidded more than 600 points as the widening pandemic stoked fears that travel restrictions and other uncertainties could dent global growth.
The U.S. market, which had calmly been setting record after record, suffered its worst January since 2016 and its first monthly loss since August.
Technology companies, which do a lot of business with China, led the losses. Airlines fell after Delta and American suspended flights to and from China. The sell-off erased the S&P 500's gains for January and gave the benchmark index its biggest weekly loss since August.
The Associated Press contributed to this article.