In a surprise move, the City Council speaker, Christine Quinn, plans to introduce a compromise bill to alter the 421-a tax abatement program, setting off a scramble for support among competing proposals from the Bloomberg administration and a coalition of council members.

Ms. Quinn said her bill is still being worked out, but it signals an attempt to broker a deal between the mayor’s proposal and the more radical changes that some lawmakers are pushing.

Originally created in 1971 to spur residential construction, the 421-a program gives tax breaks to developers, but there is widespread agreement that the system has become outdated. The program provides added incentives to developers that build affordable housing, and officials are now debating how to expand that requirement without affecting the housing boom.

The current version of 421-a expires at the end of 2007, and the council must act to change it a year in advance, meaning lawmakers and the administration have only a month to reconcile differences on a range of issues.

Mayor Bloomberg’s proposal stems from recommendations issued by a city task force last month. It would limit the tax breaks to developments that include affordable housing in certain areas of Manhattan, Queens, and Brooklyn, but many council members want to expand the affordable housing requirement citywide, citing the need for more low- and middle-income options. Under the Bloomberg plan, developments in Manhattan south of Harlem, along the East River in Queens and Brooklyn, and in parts of Brooklyn Heights and DUMBO must designate 20% of the units for families earning no more than 80% of the area median income in order to qualify for the tax break.

“The administration’s proposal is weak,” Council Member Annabel Palma of the Bronx said. “It leaves out areas around the city that will benefit from affordable housing.”

Along with Council Member David Yassky of Brooklyn, Ms. Palma led a rally of housing advocates in support of their proposal, which would require developments in all five boroughs seeking inclusion in the 421-a program to designate 30% of units to families earning a maximum of 50% of the area median income. Mr. Yassky criticized the administration’s proposal, saying it would subsidize luxury development at the expense of taxpayers.

While the real estate industry was not thrilled with the Bloomberg administration’s 421-a proposal, the Palma/Yassky bill is a “farce,” the president of the Real Estate Board of New York, Steven Spinola, said. Increased affordable-housing requirements, he said, would further hamper housing construction. “Whatever they do I think is going to weaken the housing production in the city of New York in the next couple of years,” Mr. Spinola said.

Supporters of the Palma/Yassky bill said 21 of the council’s 51 members had signed on to the measure as of last night.

The speaker said she had met in recent days with 35 council members, along with administration and industry officials. She plans to introduce a bill with the chairman of the Housing and Buildings Committee, Erik Martin Dilan, at next week’s council meeting.

The administration is open to negotiation, a spokesman for the Department of Housing Preservation and Development, Neill Coleman, said. “We’ve certainly seen the task force recommendations as a basis for discussion,” he said. “We’re very happy to continue those discussions.” Still, Mr. Coleman said the current council proposal to expand the affordable-housing requirement citywide was “extreme.”

Despite the large number of lawmakers signing on to the Palma/Yassky bill, council sources said they expect the speaker to be able to command broad support when she finalizes her plan, which she indicated would seek a middle ground between the two current proposals. Other lawmakers may introduce separate bills next week as well, and several said they were waiting to see what Ms. Quinn came up with.

Ms. Quinn has developed a productive relationship with the mayor, frequently agreeing to compromises on legislation during her first year as speaker. While the various sides are far apart at the moment, she said she was confident the council would meet next month’s deadline.