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State officials and mayors critical of the federal response to the coronavirus pandemic began imposing the most severe emergency measures to date on Sunday, with four governors effectively forcing restaurants, bars or other businesses to shut their doors.

As the country braced for its first full week of widespread school and business closures, President Trump and other administration officials again gave mixed and sometimes confusing messages about the dangers ahead. At the White House, Trump told Americans to “relax” and stop panic-induced purchasing.

“We’re doing great. It will all pass,” he said.

Confirmed cases of the novel coronavirus jumped by nearly a third in just 24 hours — to 2,900 by Sunday, Vice President Pence announced. In Europe, Italy recorded its deadliest 24-hour period since its first cases emerged in late February — 368 deaths, up 25 percent from the previous day. That country’s death toll now exceeds 1,800.

Despite such alarming trajectories, and a new recommendation from the Centers for Disease Control and Prevention that Americans cancel or postpone events of 50-plus people for the next eight weeks, some Republican lawmakers still shrugged off the urgent warnings.

Rep. Devin Nunes (R-Calif.), a close Trump ally, encouraged Americans to go out dining or drinking, directly contradicting public health officials’ admonitions for social distancing to slow the rate of infection.

“It’s a great time to go out and go to a local restaurant, likely you can get in easy,” Nunes told Fox News viewers. “Let’s not hurt the working people in this country . . . go to your local pub.”

In California, Nunes’s endorsement was countered hours later by Gov. Gavin Newsom (D), who asked all bars, clubs and wineries to close. He recommended that restaurants cut their occupancy in half to minimize patrons’ contact. He also called on everyone older than 65 or with chronic conditions to self-quarantine at home.

Ohio Gov. Mike DeWine (R) and Illinois Gov. J.B. Pritzker (D) went a major step further, shuttering all the bars and restaurants in their states. The move in Illinois lasts through the end of March. In Ohio, it is indefinite.

“How long this order will be in effect we don’t frankly know,” DeWine said. “It will be in effect as long as it needs to. . . . Delay means more people will die.”

Massachusetts Gov. Charlie Baker (R) even banned gatherings larger than 25 people, which will affect a wide swath of public and community events, sports games, fitness clubs and theaters. He also announced that, starting Tuesday and lasting until April 6, bars and restaurants can offer food only for takeout or delivery. In the worst-hit part of the country, Washington state Gov. Jay Inslee (D) took a similar approach with an emergency proclamation that will close all bars and nightclubs, prohibit dining-in service at restaurants and restrict gatherings to less than 50 people.

These actions came after social media photos and posts showed people packing bars and restaurants around the country over the weekend. Federal health authorities have recommended Americans avoid crowded places, work from home and self-isolate to slow the potential spread of infection.

New York Gov. Andrew M. Cuomo (D) urged Trump to activate the Army Corps of Engineers to prepare emergency medical facilities nationwide. In New York City, Mayor Bill de Blasio (D) said he will order bars, clubs and movie theaters to close and, beginning Tuesday, will only allow pickup and delivery from restaurants.

And in Puerto Rico, Gov. Wanda Vázquez Garced closed nonessential businesses and enacted a curfew in an attempt to contain the virus on the island.

The vice president on Sunday declined to answer a question on how Americans can best practice social distancing and whether restaurants and other businesses nationwide should close, saying only that there will be new guidance released on Monday.

“We will have updated guidelines tomorrow,” Pence said at the coronavirus response team’s late afternoon briefing.

Anthony S. Fauci, director of the National Institute of Allergy and Infectious Diseases, also declined to elaborate on the topic. But he didn’t back away from earlier comments.

“I meant everything I said this morning on the shows,” said Fauci, who appeared on all five Sunday morning news shows and urged “a dramatic diminution of the personal interaction that we see in restaurants and bars.”

The sweeping measures state measures leave business owners and employees throughout the country in a predicament without precedent in recent memory. In announcing Ohio’s closures, DeWine sought to throw workers there a lifeline: He said he hoped restaurants and bars would stay open to offer delivery and takeout options.

“Look, you can walk in, buy a doughnut and coffee and walk out, that’s okay,” he said. “Some of our great places to eat I know have carryout. Maybe more will be encouraged to do this.” Still, DeWine acknowledged that small business owners and their staffs will be hurt.

He apologized for the suffering he was about to inflict — but insisted he had to act now to ensure that Ohio’s health-care system does not break down under the pressure of an ever-rising tally of coronavirus patients. As of Saturday afternoon, the state had seen 36 confirmed cases, with at least 350 awaiting pending test results, according to Ohio Health Department Director Amy Acton.

Escalating financial worries also prompted a Federal Reserve announcement late in the day. Ahead of Wall Street’s opening on Monday, the central bank said it would slash interest rates to zero and buy at least $700 billion in government and mortgage-related bonds in an emergency action to shore up the economy. The decision was its most dramatic since the 2008 financial crisis and represents a major intervention aimed at stabilizing financial markets by keeping borrowing costs as low as possible for businesses crippled by the pandemic.

“That’s really good news,” Trump responded. “That’s really great for our country. We’re very happy. I think that people in the market should be very thrilled.”

The president’s declaration that he would suspend “all travel” from Europe beginning midnight Friday night appeared to have left many U.S. travelers with the mistaken impression that they were at risk of being stranded abroad. Homeland Security officials scrambled to clarify that U.S. citizens, permanent residents, their families and many other travelers would be exempt and could return any time, but many Americans still rushed to catch flights.

Travelers arriving at major U.S. airports late Saturday from Europe’s worst hotspots were herded into hours-long queues for cursory health screenings. Images on social media — of people packed elbow-to-elbow, in scenes that resembled the early stages of Trump’s 2017 travel ban on many Muslim-majority countries — stoked outrage and concerns that the administration’s latest travel restrictions could facilitate the outbreak they were meant to contain.

The delays were particularly acute at Chicago O’Hare International, and Chicago Mayor Lori Lightfoot (D) aimed a sharp criticism at the administration.

“If you do not listen, and you do not bring us along on the journey first, you’re going to see more disasters like last night that are solely the responsibility of the federal government not listening,” she said.

By Sunday afternoon, reported waits were much shorter and screening procedures much smoother.

In a statement, U.S. Customs and Border Protection termed those long waits at international terminals “unacceptable.” Officials attributed the delays to the agency’s “partners,” without addressing questions about whether it had increased staffing in advance at the 13 major U.S. airports that are the only places flights from Europe currently can land.

Chad Wolf, the acting secretary of Homeland Security, said the situation had been “fixed” and that wait times were now averaging half an hour.

At Washington Dulles International Airport, arriving passengers reported no problems or unusually long waits getting through customs Sunday afternoon. However, several said they were surprised that they hadn’t faced more stringent health screenings and were asked instead to fill out a basic declaration form asking if they’d been to any countries subject to restrictions.

Fahim Hayat said he had expected hours of delay after arriving on a flight from Amsterdam. Instead, he breezed through screening in 20 minutes. No one checked his temperature, he said, and there was no hand sanitizer in the arrival hall, where passengers were freely sharing pens as they filled out immigration forms.

“I’m a clean freak, so there were a lot of things I would have thought about twice,” he said.

Other elements of daily life continue to contract.

Classrooms in New York City, which has the nation’s largest school district, will go dark on Monday, joining a cascading number of states and big cities that have shuttered their schools amid coronavirus concerns. De Blasio said Sunday that the schools would be closed at least through April 20 and possibly through the end of the academic year.

In Maryland, Gov. Larry Hogan (R) issued an emergency order to close all Maryland casinos, racetracks and simulcast betting facilities to the general public indefinitely.

“This situation continues to evolve and will escalate rapidly and dramatically,” Hogan said. “These are unprecedented actions in an extraordinary situation, but they could be the difference in saving lives and keeping people safe.”

DeWine also said Sunday that schools in Ohio could remain closed for the rest of the semester.

The new workweek will open with many white-collar private-sector employees telecommuting. But hundreds of thousands of federal workers are scheduled to report at their offices Monday, creating widespread anxiety. Many say they have received little guidance.

The Trump administration has told federal agencies that “only mission-critical travel is recommended at this time” because of the pandemic. That directive, issued Saturday by the White House’s Office of Management and Budget, primarily applies to domestic travel because federal workers fell under previous general restrictions on international travel. Under the memo, individual agencies are to determine whether travel is needed for “mission-critical” reasons.

Katie Zezima, Laura Meckler and Heather Long in Washington; Mark Guarino in Chicago; and Chico Harlan in Rome contributed to this report.