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CHICAGO — Airports nationwide were thrown into chaos this weekend as workers scrambled to roll out the Trump administration’s hastily arranged health screenings for travelers returning from Europe.

Scores of anxious passengers said they encountered jam-packed terminals, long lines and hours of delays as flights from more than two dozen European countries were routed through 13 of the busiest travel hubs in the United States. Airport workers queried them about their health and instructed them to self-quarantine as part of the “enhanced entry screenings” announced Friday to slow the spread of the coronavirus.

As confusion and anxiety spread, the situation threatened to deepen the crisis for the administration, which has struggled to mount a coherent response to the pandemic or convey a consistent message to the public about what the federal government is doing to mitigate the outbreak.

Shortly after taking effect, the measures intended to prevent new infections in the United States caused conditions that facilitate the spread of the highly contagious virus, with throngs of people standing shoulder to shoulder — in some cases for several hours.

Chicago Mayor Lori Lightfoot (D) sharply criticized the federal government during a news conference Sunday at O’Hare International Airport, saying passengers’ safety was “seriously compromised” and warning of “more disasters” to come if communication does not improve.

Administration officials acknowledged that the 40,000 passengers returning from Europe on Saturday initially caused enormous strain on the system. Acting homeland security secretary Chad Wolf conceded that the waits were “unacceptable” but said during a Sunday evening news conference at the White House that the situation had quickly improved, with average wait times dwindling to 30 minutes across 13 affected airports.

The upheaval left travelers with questions about the rollout of the new measures. Many expressed surprise Sunday that the health checks were not more stringent and generally did not include temperature checks.

Mike McGowan, of Alexandria, Va., said he and his family breezed through the line at Dulles International Airport outside of Washington after declaring that they had not been to any of the European countries with travel restrictions — even though there were passengers on his flight who had connected through London from Spain and other parts of Europe with higher numbers of infections.

Fahim Hayat, who waited only 20 minutes to pass through customs and immigration, said that no one checked his temperature, that there was no hand sanitizer available and that passengers were freely sharing pens as they filled out immigration forms. “I’m a clean freak,” said the 29-year-old from Dumfries, Va. “So there were a lot of things I would have thought about twice.”

The scenes from Saturday night, though, captured in an outpouring of angry social media posts, were reminiscent of the chaotic implementation in early 2017 of President Trump’s travel ban targeting citizens from predominantly Muslim countries, which triggered confusion and protests at U.S. airports as travelers from the Middle East were detained or sent back with almost no warning.

In a tweet posted Sunday after midnight — several hours after reports of clogged terminals started circulating — Wolf acknowledged the backup and said the Department of Homeland Security was rushing to add screening capacity to help airlines expedite the process.

“I understand this is very stressful,” Wolf said on Twitter. “In these unprecedented times, we ask for your patience.”

U.S. Customs and Border Protection issued a statement Sunday, saying, “With this national emergency, there will unfortunately be times of disruption and increased processing times for travelers.”

Sen. Richard J. Durbin (D-Ill.), citing the eight-hour waits some passengers experienced, accused the Trump administration of being unprepared, and Sen. Edward J. Markey (D-Mass.) wrote a letter to top CBP officials and to the Centers for Disease Control and Prevention asking how authorities intended to “prevent the spread of this dysfunction.”

A White House official, who spoke on the condition of anonymity because that person was not authorized to speak publicly, said Sunday that CBP was deploying new officers to address the airport lines, and Wolf said later that the issues were “fixed.”

The chaos came as the United States prepared to extend its travel ban to the United Kingdom and Ireland starting overnight Monday, bringing the total number of restricted countries in Europe to 28.

At Dallas-Fort Worth International Airport, people spent hours in the cramped terminal waiting to fill out questionnaires from the CDC. Dorothy Lowe of Longview, Tex., said she stood in a customs line from 4 p.m. until after 7 p.m. Saturday after returning from a trip to Mexico.

“We’re all being herded in the same line, standing side by side,” Lowe told WFAA-TV. “I’m less concerned about having to stand here for the amount of time that I am and more concerned about where the people are traveling from that are around me and what they may or may not have been exposed to.”

Travelers reported similar problems at New York’s John F. Kennedy International Airport. “Just waiting in a very long line with thousands of people to clear Customs at JFK T4,” one user wrote on Twitter. “Not sure who’s really taking things seriously.”

After reading about the long lines at O’Hare on Saturday, 34-year-old Matt McIlvane said he was “preparing for the worst” coming back from Austria. But the Joliet, Ill., resident found just a 40-minute wait to get through customs.

“It seems like a well-oiled machine now,” he said.

Travelers nonetheless described their anxiety as they left trips cut short amid the virus’s rapid advance around the globe. Alma Garcia, 59, of Chicago had planned to spend her 60th birthday in Greece — but she and her friend had to exit the country early once the government shut down all restaurants and shops. They feared airports would be next.

Although their trip through customs lasted only about an hour, they worried it would take longer after experiencing a 13-hour layover in London because of a delayed flight.

“It was nerve-racking,” she said.

Hawkins, Knowles and Shaver reported from Washington. Nick Miroff, Hannah Natanson and Philip Rucker contributed to this report.