The S&P 500 closed at 4,410, up 0.3%, while the Dow and Nasdaq rose 0.3% and 0.6%.
Shares are mixed in Europe and Asia after the World Health Organization declared the outbreak of a new virus that has spread from China to more than a dozen countries a global emergency.
Major stock indexes are moving broadly higher on Wall Street after President Donald Trump said China was willing to reopen talks on trade.
Stocks are moving sharply higher after Federal Reserve Chairman Jerome Powell suggested the central bank might consider a pause in its interest rate hikes next year.
The Dow Jones industrial average gained 567 points, or 2.3%, recouping nearly half of the 1,175-point plunge it took the day before.
Major U.S. stock indexes managed to post tiny gains in a quiet day of pre-holiday trading.
Tumult in China triggered the worst opening week for U.S. stocks in history, and this week investors could get plenty more to worry about.
Major U.S. stock indexes are back at record highs after a turbulent month. Stocks rallied in the U.S. and overseas after Japan's central bank surprised investors with a new round of economic stimulus.
Stocks are ending sharply lower after a late-afternoon slide. The Dow Jones industrial average slumped 222 points, or 1.4%, to close at 16,321 Monday.