The city’s largest public employees union, District Council 37 of the American Federation of State, County and Municipal Employees, is pressing the City Council to join Mayor Bloomberg in ending a residency rule that requires 45,000 of the union’s members to live in New York City.

But the proposal is facing fierce opposition from the usually labor-friendly City Council. Some council members say city jobs should be reserved for city residents.

Union leaders have argued it is unfair to force employees to stretch their salaries to pay for costly housing in the city when there are more affordable options available in the outlying areas. They propose that their members be allowed to leave the city and reside in the counties of Nassau, Suffolk, Westchester, Rockland, Orange, and Putnam and aren’t taking the council’s resistance lightly.

The union indicated earlier this year that stances on the residency question will be crucial for City Council members seeking union support in upcoming elections.

“Our patience is running out,” the union’s executive director, Lillian Roberts, said yesterday. “We are very, very serious about this. It is going to impact anyone who can’t understand they are hurting us.”

Critics of the proposal say it would make it more difficult for New Yorkers to land city jobs, since they would be competing against applicants not only from the city, but from the six surrounding counties. Some council members consider the jobs a ticket to the middle class.

“It dries up employment opportunities for the people in New York City. It makes the field much more competitive,” a council member who represents Harlem, Robert Jackson, said. “I don’t want people from outside to be taking city jobs.”

Ms. Roberts will be joined by nearly one dozen labor leaders on the steps of City Hall today to call on the council to lift the residency requirement.

A council member who represents Queens and who is the chairman of the Civil Service and Labor Committee, Joseph Addabbo, said he would be comfortable with the bill if at least one of two changes were made: a requirement that job seekers be city residents when hired or a stipulation that the residency requirement be lifted for current employees only, but not those hired in the future.

Mr. Addabbo is one of 23 council members who signed on to sponsor the residency bill, which was introduced last year at Mayor Bloomberg’s request. Mr. Addabbo said many of those who initially signed off on the plan did so without fully understanding the consequences.

“The bottom line is we have to protect city jobs for city residents,” he said.

A spokesman for Council Speaker Christine Quinn, James McShane, wrote in an e-mail message that Ms. Quinn “looks forward to having an open dialogue with her City Council colleagues and DC 37 leadership.” She has not publicly taken a position on the bill.

In July 2006 the Bloomberg administration agreed to end the longstanding requirement that this group of city employees live in the five boroughs as part of its tentative contract agreement with the union.

When announcing the tentative agreement, Mr. Bloomberg reportedly said that the restrictions were adopted nearly 20 years ago “when many middle class families were leaving New York for the suburbs, and a lot has really changed since then.”

“One of our big problems is a lack of housing, and laws that exacerbate that problem don’t really accomplish anything. Those are laws that were appropriate in a different period, back when the city was not doing well,” he said, according to a report in Newsday.

Mr. Bloomberg’s position marked a reversal from an earlier stance on residency requirements for city employees. In 2005, he opposed an ultimately successful effort by Sanitation Department employees to overturn a rule that restricted where they could live. New York’s teachers, firefighters, police officers, and now, sanitation workers, are not required to live in the city.

Ms. Roberts said her members should have the same rights as other city employees. The DC 37 members affected by the residency requirement earn $30,000 a year on average, she said. Three hundred of them have lived in homeless shelters at one time and 15,000 reside in public housing projects, she added.

Ms. Roberts is not predicting an exodus of public employees from the city if the bill is approved, but she said that many of her members would like the opportunity to leave.

“The union has been asking for this for 20 years and finally we got a mayor who was sensitive to our needs,” she said. “Now, we are stuck with the City Council.”