Ohio ordered restaurants and bars to close starting Sunday night and Maryland ordered casinos, racetracks and betting facilities to close “indefinitely.” Starbucks said it would close some stores in malls and cities with outbreaks, including New York and Seattle, and shift to a “to-go” model in all other locations.

Gov. Gavin Newsom of California called for everyone 65 and older to shelter at home and asked all bars, nightclubs and wineries to close.

Dr. Anthony Fauci, the director of the National Institute of Allergy and Infectious Diseases, said that people were “going to have to hunker down significantly more than we as a country are doing.”

He suggested a 14-day national shutdown might eventually be warranted and urged people to practice social distancing. “There are going to be people who are young who are going to wind up getting seriously ill,” he said.

There was chaos over the weekend at some of America’s biggest airports, as the U.S. government rushed on Saturday to enact Mr. Trump’s restrictions on travel from Europe. In Dallas, travelers posted photos on Twitter of long winding lines in the airport. In New York, customs agents in paper and plastic masks boarded a flight from Paris. And in Chicago, where travelers reported standing in line for hours, Gov. J.B. Pritzker of Illinois tagged Mr. Trump in a series of angry tweets about the long waits, saying, “The federal government needs to get its s@#t together. NOW.”

At a news conference on Sunday afternoon, Mr. Trump said he had held a phone call with chief executives of several food suppliers who said they were committed to staying open through the pandemic. He said the call was “very reassuring” and said there was no need to “hoard” essential food supplies.

“You don’t have to buy so much, take it easy, just relax,” Mr. Trump said. “We’re doing great, it all will pass.”