But a series of laws passed by the City Council over the past two years sought to restrict this cooperative agreement.

And according to new city statistics, the laws appear to be achieving their goal, prompting celebration — albeit guarded — among immigrants’ advocates.

From July, when the most recent of the restrictive laws went into effect, to September, city officials responded to 904 federal hold requests, known as detainers, according to the statistics. Of those detainers, the city declined to honor 331, or 37 percent.

In contrast, until the laws were passed, the city customarily honored every detainer, according to city officials.

“We feel good about the impact that this legislation has had because it has stopped the deportation of a lot of New Yorkers,” Javier H. Valdes, co-executive director of Make the Road New York, an advocacy group, said on Thursday.

“Our hope,” he said, “is that with the new administration we can increase the number of New Yorkers who will not be turned over to immigration.”

Even with the new city laws, New York’s restrictions are still not as tight as those of other major cities, like Chicago and Washington, advocates said.

Cooperation between local governments and federal immigration authorities has been a deeply contentious issue around the United States.

Some jurisdictions, convinced that the federal government has not done enough to enforce immigration laws, have increased their role in immigration enforcement. But others, concerned about the impact of deportations on their communities, have tried to put distance between themselves and the immigration machinery of the federal government.

Much of the recent debate has surrounded the federal Secure Communities program. The initiative allows Homeland Security officials to more easily compare the fingerprints of every suspect booked at a local jail with those in its files. If they find that a suspect is a noncitizen who is in the country illegally or has a criminal record, they may issue a detainer.

The Secure Communities program, a cornerstone of the Obama administration’s immigration enforcement strategy, has been vehemently opposed by some elected officials around the country, who have sought to limit their jurisdictions’ participation.

In November 2011, the City Council passed a law that narrowed the range of detainers the city would honor. Among other terms, the law prevented correction officers from transferring immigrants to federal custody if the inmates had no convictions or outstanding warrants, had not previously been deported, were not suspected gang members or did not appear on a terrorist watch list.

The effect on the detainer system was immediate: Correction officials went from routinely honoring all detainers to, according to the recently released statistics, about 75 percent of them.

In February, the Council imposed additional restrictions, including blocking detainers for immigrants facing all but the most serious misdemeanor charges, like sexual abuse, assault and gun possession.

Under these new guidelines, the percentage of detainers the city rebuffed rose to about 37 percent from about 25 percent. The rates may have even been higher had the federal government not concurrently altered its own detainer policy, limiting the range of immigrants it would seek custody of.

Still, immigrant advocates said they would press for more restrictions and have reoriented their lobby toward Mayor-elect Bill de Blasio, who has vowed to end the city’s cooperation with federal immigration detainers except for detainees convicted of “violent or serious felonies.”

Newark, San Francisco and Santa Clara, Calif., are also among the cities that have more restrictive detainer policies than New York, according to Emily Tucker, staff attorney at the Center for Popular Democracy, an advocacy group in New York.

“New York City can do much better than these numbers show we are doing at the moment,” she said.

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