Following days of pressure, Mayor Bill de Blasio announced plans to close the nation’s largest public school system.

New York City’s public school system, the nation’s largest, will begin shutting down this week, by far the most far-reaching and disruptive measure the city has taken yet to slow the spread of the coronavirus.

The city’s vast system of 1,800 schools now faces its most serious challenge in decades, as it embarks on a mass closure that could potentially last through the end of the school year.

“This is not something in a million years I could have imagined having to do,” Mayor Bill de Blasio, appearing visibly distraught, said on Sunday, adding that it was an “extraordinarily painful” moment for city schools.The closures will alter the lives and routines of 1.1 million children, 75,000 teachers and well over 1 million parents, and will no doubt prompt broader upheaval in a moment of profound anxiety for New Yorkers. Mr. de Blasio said that the schools will be closed on Monday for all students and staff, but teachers will be asked to report to work later in the week for training on remote learning. By March 23, the city will move to remote learning, and the system will be closed except for several dozen school buildings throughout the city, which will be used as “learning centers” to support the children of essential city workers like health care employees.

Schools will be closed until at least April 20, after the upcoming spring break, but could stay closed for significantly longer, Mr. de Blasio said.

City school buildings will remain open this week for children to pick up food, and then the city will find alternative sites for students who need food to receive it. Students who do not have computers at home will be lent laptops, and the city will work on helping students who do not have internet access get online.

All public schools in Westchester and Long Island will also close, Gov. Andrew M. Cuomo said Sunday.

The mayor and Mr. Cuomo had resisted closing the city’s schools even as other states shuttered their public schools, and urban school districts, like Los Angeles and Seattle, did the same.

But in recent days, a growing chorus of local politicians, public health experts, parents and educators have ramped up the pressure on the city to shut down schools. By Sunday afternoon, even Mr. Cuomo said the city schools should close within 24 hours, as soon as the city came up with a plan for child care and food.

Student attendance has plummeted as nervous parents have kept their children at home. Teachers concerned about the virus organized “sick outs” and flooded Twitter and 311 with pleas to shut down schools. And as the outbreak continued, each day seemed to bring another major set of school closures in cities and states with smaller outbreaks than New York’s.

New York City’s school system stands apart from every other in the country for its sheer size and particularly vulnerable student population, including enough homeless children — 114,000 — to fill an entire small city school district. Even if only half of New York City’s students reported to school, the district would still be larger than any in the country except for Los Angeles Unified, which announced on Friday that its schools would close for at least two weeks. Gov. Philip D. Murphy of New Jersey said on Sunday that state’s public school system would close imminently.

Public health experts agree that effective closures would have to last for the length of the virus, which could take months. And students getting together in their homes or other places outside of school could diminish the effectiveness of closures, experts said. Mr. de Blasio was blunt about the prospect of keeping children apart in the weeks and months ahead.

“We’re not going to convince teenagers not to gather,” he said.

or just beginning to make improvements in school. About 20 percent of children have special needs, some of which are advanced, and many of those students get services at school they cannot get at home. About three-quarters of city students are eligible for free or reduced price meals at school.

Annual standardized math and English exams scheduled for this spring will almost certainly have to be delayed, education officials said.

And there are hundreds of thousands of public school parents who do some of the city’s most essential work: staffing public hospitals, driving city buses and subways and caring for older people.

The large-scale, indefinite school closures leave New York City in uncharted territory. A handful of city schools closed during the 2009 H1N1 flu epidemic, and the city closed its school system for a week after Hurricane Sandy in 2013, with some schools remaining shut for longer.

On Sunday evening, New York City parents reacted to the news with a mix of confusion and concern.

“Are we going to be home schooling? It’s something I always wanted to try,” asked Belinda Blum, who lives in Crown Heights, Brooklyn, and has two daughters in public school. Ms. Blum said she wanted to make sure that her daughters still had structure in their day, even if they were learning from home.

Gary Purdy, who has two children in the public school system, said he didn’t know how the city would decide to reopen schools.

“Are you going to test every single school, every single person in the city?” Mr. Purdy, also a Brooklyn resident, asked.

In Harlem, Alicia Taylor said she had already made a backup plan: She was preparing to take her children to North Carolina, where they could be close to family and have room to spread out.

She said she wasn’t sure how her children would be educated remotely. “What the hell is everyone going to do?” she asked.

Ashley Southall and Matthew Sedacca contributed reporting.