But the tougher fight was financial. Mr. Ali, 78, had meager savings, and his wife had not worked since they immigrated to the United States from Pakistan in 2006. So the couple depended on his monthly Social Security check of less than $600.

“It was extremely difficult,” he said, especially putting enough food on the table.

These are increasingly familiar concerns within New York City’s growing immigrant population.

As is the case in the rest of the country, the city’s residents are skewing older. Yet a new study, released Thursday, reveals that immigrants are the driving force behind this trend, posing enormous challenges to local government agencies and social service organizations.

From 2000 to 2010, the number of immigrants in the city aged 65 and older increased by about 30 percent while the corresponding native-born population dropped by 9 percent, according to the study by the Center for an Urban Future, an independent research organization in New York.

The foreign-born now represent 46 percent of the city’s population aged 65 and older, a proportion far higher than their share of the city’s overall population (37 percent).

“I think it’s the biggest demographic trend that nobody is talking about,” said Jonathan Bowles, the center’s executive director.

Besides being one of the fastest-growing demographic groups, older immigrants are also among the most vulnerable. “Many in this group are not only poised to strain the social safety net but fall through it entirely,” the study said.

On average, older immigrants have far lower incomes and far smaller retirement savings than older native-born residents, and they receive fewer benefits from entitlement programs like Medicare and Social Security. Nearly 24 percent of all older immigrants in the city live in poverty, compared with 15 percent of their native-born counterparts, the study said.

In addition, language obstacles conspire with a lack of education and cultural barriers to keep many older immigrants from finding out about, and seeking help from, government agencies and community-based advocacy groups.

Last year, Mr. Ali found some relief from his struggles at the Council of Peoples Organization, a community group focused on South Asian Muslims that had opened a senior center at its office in Midwood, Brooklyn. He now spends his days there, eating free meals, making friends, watching Pakistani satellite television programs and “hanging out,” he said through an interpreter. The center has also helped him and his wife apply for additional government assistance and get medical help.

The organization’s executive director, Mohammad Razvi, said the center opened last year after clients began asking if they could take some of the canned food that had been donated for disaster relief in Pakistan.

With its extensive public transportation networks, concentration of health care centers, array of immigrant enclaves and proliferation of immigrants’ services groups, New York City can be a relatively accommodating place for immigrants to grow old.

Yet in interviews, advocates for older immigrants said that the needs of the population were far from being met and that more financing, from both public and private sources, was needed to meet current, and especially future, demand.

There are now at least 463,000 immigrants aged 65 and older living in New York City, the largest population of its kind in any city in the United States, according to the report, which was based in part on census data.

The growth is largely attributable to the aging of the people who arrived in the United States during the 1980s and 1990s, decades that saw a sharp increase in immigration, Mr. Bowles said.

Among the array of challenges that these immigrants now face, poverty arguably looms largest; about two out of every three elderly people in New York living below the poverty line are immigrants, the study said.

Immigrants tend to earn significantly less over the course of their working lives than native-born people and therefore receive less in benefits from Social Security, and many do not qualify at all for the program or have not enrolled, the study said.

Kit Fong Lee, 74, who volunteers at a senior center in Lower Manhattan run by the Hamilton-Madison House, said the center’s clients, most of whom are Chinese immigrants, received Social Security benefits of, on average, about $600 a month, around half the national average. Some clients scrape by collecting soda cans on the street, she said, or by relying on relatives.

The most significant barrier preventing older immigrants from taking advantage of social services in the city is their inability to communicate with service providers in a language they know well, the study asserted.

“When I go to Manhattan, I can sometimes get lost,” Soon Kim, 88, said through an interpreter. “When I get sick I can’t describe how sick I am.” For 26 years, Ms. Kim has been a regular at a senior center in Corona, Queens, run by Korean Community Services of Metropolitan New York.

Language barriers can lead to social isolation, advocates said, which in turn can lead to mental illness and suicide.