“If you live in our city, you’re more likely to understand our community,” Mr. Jeffries said in front of Police Headquarters on Sunday afternoon.

Paul J. Browne, the Police Department’s deputy commissioner for public information, said that about half of the officers associated with the offensive comments live outside the city. Sixty percent of the current Police Academy class lives in the city, Mr. Browne added. Under current rules, officers are required to live either in one of the five boroughs or in one of six nearby counties: Nassau, Suffolk, Westchester, Rockland, Putnam or Orange.

Patrick J. Lynch, president of the Patrolmen’s Benevolent Association, said the organization opposed the proposed measure. Most officers who do live in the five boroughs, he said, “have to work a second job or must have their spouse work in order to afford to live in the city they protect.”

The legislation would not require officers who already live in one of those counties to move, said Mr. Jeffries, a Democrat whose district in Brooklyn includes the site of much of the parade. Only future recruits would be subject to the law.

Mr. Jeffries was joined by Representative Yvette D. Clarke and Councilwoman Letitia James, both Democrats of Brooklyn. Ms. James likened the Facebook comments to “basically police terrorism, when you talk about bombing individuals.”

Last week, Police Commissioner Raymond W. Kelly and Mayor Michael R. Bloomberg each condemned the comments. “It’s totally inappropriate, and I can use lots of other words to describe it,” the mayor said.

Rickford Burke, president of the Caribbean Guyana Institute for Democracy, which is based in New York, said words alone would not placate the community’s concerns. “We are not asking for a slap on the wrist,” he said. “The lives of Caribbean Americans are in danger with individuals like these on the police force.”