Facing a population explosion in New York City’s shelter system driven largely by a monthslong flood of migrant asylum seekers, Mayor Eric Adams on Wednesday seemed to call into question the city’s unique “right to shelter,” which has been guaranteed by court order for over 35 years.

New York is the only place in the country where every person who seeks a bed must be given one. And Mr. Adams, citing a “new and unforeseen reality” that “no city official, advocate or court ever could have contemplated” in which 11,000 migrants have entered the shelter system since May, said that the system was “nearing its breaking point.”

As a result, he said, “the city’s prior practices, which never contemplated the busing of thousands of people into New York City, must be reassessed.” The Republican governor of Texas, Greg Abbott, has been sending buses of migrants, mostly from South and Central America, up from the border to New York as part of a campaign to push Democrats to tighten immigration.

Pressed on whether Mr. Adams was specifically suggesting an end of the right to shelter, his press secretary, Fabien Levy, at first echoed the mayor, saying: “No city official, advocate, or court ever could have contemplated the unprecedented crisis. We’re saying the whole system needs to be reassessed.”

Later in the day, Mr. Levy added, “Every New Yorker has a right to shelter. We are not disputing that.”

Still later, he said: “We’re not trying to get rid of right to shelter. Right to shelter is law.”

The administration’s statements came the day after the city failed to offer beds to 60 of the hundreds of men who arrived on Monday at the men’s intake shelter on East 30th Street in Manhattan, the first lapse of that magnitude in over a decade.

The math of migration has been relentless and unforgiving. Since June, the population of the city’s main shelter system, which was already having problems moving people into permanent housing, has grown by 20 percent.

Just since Aug. 9, the population of the main shelter system has grown by more than 5,000, from 51,000 to nearly 56,000, an increase of nearly 10 percent. In the past week, the shelter population has jumped by over 1,000.

If the city were to consider undoing the right to shelter, its path would not be simple. Its lawyers would need to go to court in two different cases from the 1980s — one that established the right for single adults, and another that enshrined it for families — and ask to be relieved of its obligation to provide shelter to these populations.

Any such attempt would be fought by the Legal Aid Society, which filed the litigation that led to the right to shelter.

“While we understand and appreciate the demands that the city faces, the law is clear,” the society said in a statement Wednesday. “Anyone in need of shelter, including asylum seekers, is entitled to such in New York City. This principle has been settled for decades, and is not subject to unilateral tinkering by a new administration.”

Condemnation of the mayor’s remarks from left-leaning elected officials was swift.

“Hard, unequivocal NO,” Councilman Lincoln Restler of Brooklyn wrote on Twitter. “As Gandhi famously said: ‘The true measure of any society can be found in how it treats its most vulnerable members.’ New Yorkers are proud to guarantee a right to shelter for all who need a safe place to sleep. That will not change.”

Ritchie Torres, a congressman and former city councilman from the Bronx, warned that an end to the right to shelter would force people into the streets.

“But for the right to shelter, NYC would have the same level of street homelessness as California, where homeless encampments are ubiquitous,” he wrote on Twitter.

The last mayor to try to tamper with the right to shelter was Michael R. Bloomberg. In 2008, after a battle that dragged on for years, his administration gave in.

Emma G. Fitzsimmons contributed reporting.