The legislation has already been a nettlesome issue in the Democratic race for mayor, especially for Christine C. Quinn, the Council speaker, who has faced a growing challenge to her early front-runner status. She supported the measure creating an independent inspector general for the Police Department, which passed by a vote of 40 to 11, but she opposed the other, on police profiling, which received 34 votes in favor and 17 against.

“I worry about having too much judicial involvement,” she said before casting her vote, explaining that she did not believe the profiling bill would make New Yorkers less safe.

Despite her earlier stated opposition, she allowed both bills to move forward, and on Monday presided over a so-called discharge vote — the first since the current structure of the Council was established in 1989 — to bring the legislation out of committee, where it had stalled.

The two bills were first introduced as a package last year by Councilmen Jumaane D. Williams and Brad Lander.

Mr. Bloomberg has 30 days to veto the bills. If he does so, the City Council then has 30 days from its next full meeting to hold an override vote. The mayor and the Police Department have lobbied hard against the bills in public and behind the scenes, and they appeared likely to keep up the pressure between the veto and the override vote in an effort to change the minds of supporters.

Mr. Kelly sent a letter on Tuesday to each of the Council members, arguing that the profiling bill could be used to force the removal of surveillance cameras and urging them to vote against it. “The bill would allow virtually everyone in New York City to sue the Police Department and individual police officers over the entire range of law enforcement functions they perform,” Mr. Kelly wrote.

Mr. Williams, responding to Mr. Kelly’s letter, said: “If the cameras were put in high crime neighborhoods as a response, that’s good policing. If he put them there because black people live there, that’s a problem.”