Centers for Disease Control and Prevention (CDC) director Robert Redfield said the danger was higher as a fresh outbreak would likely coincide with the flu season.
It would put "unimaginable strain" on the US health care system, he said.
The US has seen more than 800,000 cases - the highest in the world.
More than 45,000 people have so far died with coronavirus across the US, according to a tally kept by Johns Hopkins University.
California had its highest one-day rise in new cases on Monday while New Jersey, the worst-hit US state apart from New York, saw its highest increase in deaths in one day.