Monday's moves came after the S&P 500 and Dow each gained at least 3% last week while the Nasdaq Composite advanced 1.8% to close out May.

Those gains were propelled by increasing bets by traders that the global economy will successfully reopen after the coronavirus forces a shutdown of most economic activity.

Last week's gains led the major averages to their first back-to-back monthly advances since late 2019.

The Dow and S&P 500 gained 4.3% and 4.5%, respectively, for May while the Nasdaq Composite advanced 6.8%.

"Nothing that has happened since the market closed on Friday has been market positive," said Art Hogan, chief market strategist at National Securities.

"When you think about clearly we're beginning to take U.S.-China tensions seriously and you add on to that the massive amount of disruption going on in almost every major city in the country right now, none of that could be seen as market positive.".

Before May's gains, the S&P 500 surged 12.7% in April?

"The main downside risk facing stocks is a second wave of the disease," said Peter Berezin, chief global strategist at BCA Research, in a note to clients.