New York City is implementing new rules in its homeless shelters in what officials said was an effort to reduce crowding as thousands of migrants continue to arrive from the southern border.

New York is required by law to provide shelter to anyone who asks for it, but Mayor Eric Adams announced in July that adult migrants without children would be allowed to stay in city shelters for only 60 days before having to reapply for beds. The city has since issued about 13,000 notices of the 60-day limit, and for about 50 people that end date was Saturday.

On Friday, the mayor announced another change: The time limit for migrants who reapply for shelter would be just 30 days, a shift first reported by The City.

“We have now reached a point where we are full and must take action to move people seeking asylum more quickly through our shelter system,” Anne Williams-Isom, the deputy mayor for health and human services, said on Friday.

As Tropical Storm Ophelia unleashed sheets of rain over New York on Saturday, people rushed out of the Roosevelt Hotel — the city’s main intake center for newly arrived migrants, in Midtown Manhattan — and to a van where volunteers were handing out food and clothing.

Bringing back plates of chicken, rice and macaroni and cheese, many expressed confusion and anxiety about their future.

“I don’t have friends or family where I could stay,” Ibou Sene, 42, said, adding that he had arrived from Senegal four months ago and spent the last two months at a shelter a few blocks away. He was sent to the Roosevelt and had been waiting since Friday night to hear where he would be placed next.

Less than a mile away, at a migrant shelter in the Candler Building on 42nd Street, Pedro Zambrano Noguera, 58, from Tovar, Venezuela, was also worried about where he would live in the coming days.

Mr. Zambrano said he had arrived in New York in October and stayed in a succession of city shelters while waiting for his asylum application to be processed. He said he was told on Friday that he would have to leave the Candler by Sunday and could go to the Roosevelt to reapply for shelter, which he planned to do.

The Biden administration said this week that it would allow about 500,000 Venezuelans already in the United States to work legally for 18 months by offering them temporary protected status. Mr. Zambrano, who said he met Mayor Adams at an event on Aug. 9 and told him that “the key for us to get out of the shelters is work permits,” said he did not have the money or knowledge to apply.

“I have nowhere to go,” he said.

The city has offered case management services to help migrants find permanent homes. But as thousands more people cross the southern border and potentially head to New York, the scene on Saturday could be a preview of a chaotic future.

Joshua Goldfein, a staff lawyer at the Legal Aid Society, said that the city had not done a good job of communicating about the new timeline, causing “a lot of confusion.”

Without clearer instructions, some people have understood the new limits to mean that they cannot reapply again for shelter once their 30 days have expired, he said.

The move came as New York, the only major U.S. city with a “right to shelter” requirement, has struggled to house the more than 116,000 migrants who have arrived since the spring of 2022. More than 60,000 are currently in the city’s care, pushing the shelter population to a record high. The city has opened more than 200 emergency shelters.

Mr. Adams has warned, in increasingly stark terms, that the city is not prepared to assist the thousands of migrants arriving each week. This month, he claimed that the crisis “will destroy New York City.”

In addition to calling on the federal and state government to provide more funding and a “decompression strategy” to ease the burden on the city, his administration has homed in on the shelter guarantee. In May, Mr. Adams used an executive order to temporarily suspend some of the rules, including those that require that families be placed in private rooms with bathrooms and kitchens and those that set a nightly deadline for providing families with shelter beds. In the same month, he asked New York courts to relieve the city of some obligations under the agreement, which was established in a 1981 consent decree.

The announcement of the 60-day limit in July was accompanied by fliers from the city cautioning migrants that there was “no guarantee” that they would find shelter and services in New York.

Gov. Kathy Hochul, who has echoed Mr. Adams’s calls for federal aid, has also begun to discourage migrants from coming to New York. This week, she said she agreed with the mayor that the city’s guarantee to shelter should be suspended or altered.

The Legal Aid Society, which filed the litigation that led to the right to shelter, and the Coalition for the Homeless issued a joint statement strongly opposing the city’s move. The administration is due in court on Tuesday.

Inside the shelters, rumors swirl and migrants wait. Oswaldo Suárez, 36, who arrived from Caracas, Venezuela, in October, said he applied for asylum in June and had lived in the Candler for four months. After being told he had reached the 60-day limit, he arrived at the Roosevelt at 10 a.m. on Friday, and was still waiting there at 11 a.m. on Saturday.

Mr. Suárez said he needed shelter for a few more days so that he could attend his next court date. He said he had been working fast-food and plumbing jobs and was saving up to travel to Arkansas, where a friend had promised him a job in a restaurant.

“I just want a four-day extension for my court date and I’m leaving for Arkansas,” Mr. Suárez said by phone from the Roosevelt. “I have been here for more than 24 hours, and they have not attended to me.”

Andy Newman, Raúl Vilchis and Olivia Bensimon contributed reporting.