Rikers Island officials have long compiled lists of foreign-born inmates who end up in their custody. They routinely give this information to federal immigration officials, who have their own office at the jail. Deportations often follow.

With the city’s assistance, immigration authorities annually detain and deport thousands of inmates charged with a range of offenses, from misdemeanors for theft to felony drug dealing.

But now the City Council speaker, Christine C. Quinn, wants to curtail this practice by permitting the jail to cooperate with the federal immigration authorities only in limited circumstances.

Ms. Quinn is proposing legislation, to be introduced this month, that could touch off tensions over immigrant rights between the City Council and Mayor Michael R. Bloomberg, who has defended the program in the past.

“On Rikers, there is a dragnet as it relates to every foreign-born person,” Ms. Quinn said. “Stop needlessly and excessively deporting people.”

Ms. Quinn, a Manhattan Democrat who is a candidate for mayor in 2013, added that she had deep support on the City Council, saying, “I could pass this bill and override a veto.”

Opponents said the bill would improperly tie the hands of immigration officers, threatening public safety and weakening federal law.

The role of states and localities in immigration enforcement is a highly contentious issue across the United States. Some jurisdictions assert that the federal government has not done enough and have tightened their own laws. Others have characterized the federal response as overbearing, and refused to help Immigration and Customs Enforcement.

In June, Gov. Andrew M. Cuomo suspended New York’s participation in a key federal program, called Secure Communities, that makes it easier for immigration authorities to access the fingerprints of everyone booked into a local jail and to begin deportation proceedings against noncitizens.

The program at Rikers, which also operates in jails across the country, is supposed to be aimed at criminals who have committed serious offenses.

Federal authorities at Rikers place holds, or “detainers,” on noncitizen inmates they want to deport. The detainers let the city jail hold inmates for 48 hours after their scheduled release, so they can be transferred to immigration custody.

Mr. Bloomberg has defended the arrangement, calling it a public safety measure. Administration officials declined to comment on the proposed bill, saying they had not yet seen it.

Proponents of tough immigration laws said the City Council was impinging on federal jurisdiction.

“It’s a bad idea, unequivocally,” said Jessica Vaughan, director of policy studies at the Center for Immigration Studies in Washington, which favors reduced immigration. “They are essentially playing Russian roulette with public safety and putting people at risk needlessly, all because of the politics of immigration.”

Daniel J. Halloran, a Republican councilman from Queens, said he was skeptical of the bill’s legality. “You’re legislating in the realm of the federal government,” he said. “Do we even have the authority to do this?”

Ms. Quinn and other supporters of the legislation, including Robert M. Morgenthau, the former Manhattan district attorney, contend that the practice largely sweeps up inmates without criminal records — for example, people who are arrested and sent to Rikers but then have charges dropped.

In 2009, about 50 percent of the inmates flagged by federal authorities had no prior conviction, and about 20 percent had a misdemeanor as their highest prior conviction, according to statistics compiled by the City Council.

The legislation, co-sponsored by Melissa Mark-Viverito, a Democrat who represents East Harlem, and Daniel Dromm, a Democrat who represents Jackson Heights, Queens, would not end the program entirely.

It would instead forbid prison officials to hold for an extra 48 hours immigrants who were not defendants in pending criminal cases, had no prior convictions or outstanding warrants, had not been ordered deported previously and did not show up on the terrorist watch list.

That means that immigrants, even if they were here illegally, would be released if prosecutors declined to press charges against them, no matter if federal officials wanted them deported.

Luis Martinez, a spokesman for Immigration and Customs Enforcement, declined to comment on the legislation, but said the agency “will continue to pursue its mandate to protect public safety by aggressively seeking out foreign-born criminals before they can be released back into the public.”

But Andrew Friedman, co-executive director of Make the Road New York, part of a coalition that worked on the bill, called the federal policy misguided.

“It’s a tremendous step forward for the city to say clearly to the feds, ‘We’re not willing to undermine our relationship with New Yorkers in order to facilitate unjust deportations.’ ” he said.

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