Setting the stage for a showdown with the mayor, the City Council approved a new campaign finance formula yesterday that raises the amount of public money candidates can get when they are running against wealthy self-financed opponents.

The measure, which was approved in a 42-7 vote, has already become the latest political wedge between Mayor Bloomberg, who reported spending $73.9 million of his own money on his 2001 election, and the council speaker, Gifford Miller, who plans to challenge Mr. Bloomberg for his job next year.

The formula, part of a larger three bill package on campaign finance that the council approved, increases the top rate for public matching funds to $6 for every $1 raised privately, from the current $5 cap.

The measure was immediately attacked by the Bloomberg administration, which reiterated its view that the change was an excessive use of taxpayer dollars and was orchestrated to bolster Mr. Miller’s political ambitions.

The mayor’s press secretary, Edward Skyler, issued a statement calling it “one of the most self-serving, borderline corrupt laws this council has ever passed.”

Mr. Miller said, however, that the new formula is designed to prevent wealthy candidates from buying their way into office and to help grassroots contenders wage competitive campaigns.

“The bill really isn’t about the mayor. It’s not about me. It’s not about Mark. It’s not about Bill. It’s about the system,” Mr. Miller said. He was flanked by Council Member Bill Perkins, the lead sponsor of the measure, and Mark Green, the former public advocate, who lost the mayoral election to Mr. Bloomberg three years ago. All three men are Democrats. Mr. Bloomberg is a Republican.

The mayor is all but guaranteed to veto the measure and could challenge it in court, but the council is expected to override a veto. Depending on how things unfold, the law could go into effect for the upcoming election.

That timeline has come under attack by Mr. Bloomberg and by some dissenting council members, who say it is shortsighted and irresponsible. For example, Simcha Felder, a Democrat who represents a heavily chasidic area of Brooklyn, voted against the bill and vowed to opt out of the matching-fund program and not “touch a single dirty dollar.”

Proponents defended the timeline, saying the issue had been extensively examined and existing “loopholes” need to be closed. They also said the package was supported by outside “good government” groups.