“It is critically important that before you announce that you are going to ramp up that type of screening, that you develop a plan and work out all the operational details,” he said. “People who were awaiting medical screening shouldn’t have been in the same area as people awaiting passport screening.” He added: “They may have potentially placed a significant number of inbound travelers at risk of being exposed. to the virus.”

Many travelers Saturday agreed.

“I found it a little ironic they had so many people waiting in the same area,” said Genevieve Couldwell, a doctoral student who lives in Salt Lake City and flew from London to New York on Sunday. “We went through this whole process only to be kept in a situation where there might have been more exposure.”

By Sunday afternoon, the new policy appeared to be operating more smoothly in many parts of the country. At Dulles International Airport in Virginia, travelers said they had breezed through the line.

In fact, some passengers on Sunday said they were angry at what they said was not enough screening.

“They didn’t swab us, they didn’t take our temperatures, they didn’t do anything but ask us how we felt,” said Linda Cole, from Williamsburg, Virginia, who was returning from a vacation in Portugal via Heathrow.

Her friend, Carol Schrader, said one of the people on their flight had been in their hotel in Portugal and had gotten sick, though it was not clear with what.

Ms. Cole added: “They asked me if I’d been in contact with anyone who had the coronavirus. I said no, but I probably have now,” she said, a reference to their wait with other passengers to reach the screening tables.

It is also possible that shorter waits on Sunday reflected planes being less full than those on Saturday, after many people had raced to leave Europe as soon as possible in the confusion set off by President Trump’s announcement on Wednesday of restrictions on travel from mainland Europe.