A City Council committee approved a new formula for matching funds yesterday that will increase the amount of public money candidates are eligible for when they run against a wealthy opponent like Mayor Bloomberg.

The Government Operations Committee added the item to its agenda just an hour before its scheduled hearing and approved it in a 7-1 vote, catching the Bloomberg administration off guard and increasing the likelihood that it will be implemented for next year’s citywide elections.

The bill is expected to receive the approval of the full council today but has already been attacked by Mr. Bloomberg as costing taxpayers too much money. He has the power to veto it and could ultimately challenge it in court.

By adding a third tier to the two-tier system in place now, the legislation raises the cap on matching funds to $6 for every dollar privately raised, from the current $5-to-$1 ceiling.

Under current law, all candidates who participate in city-subsidized campaign financing are eligible for a $4-to-$1 match from the outset and a $5-to-$1 match when their opponents spend half of the designated spending limit. The new rate will kick in only for candidates facing opponents who spend three times the spending limit – a situation council officials say will be a rarity.

In the mayoral race, for example, candidates would be eligible for the $6 match only when their opponent spent $17.1 million, or three times the $5.7 million general-election limit.

Mr. Bloomberg, a Republican who reported spending $73.9 million to win election three years ago, criticized the move as “the ultimate backroom deal” and said it was being passed to benefit one person: the council speaker, Gifford Miller, a Democrat of Manhattan who plans to challenge him in next year’s election.

“It will help one person fulfill his political ambitions, and I don’t think that is something the public is going to find favorably,” Mr. Bloomberg said.

Mr. Miller’s chief spokesman, Stephen Sigmund, shot back quickly, with a statement saying, “Our campaign finance bill protects city elections from being purchased by one person.”

Council officials estimate the new measure will cost the city a maximum of about $4 million more. In the case of the mayoral race, the cap on the city portion would be $7.2 million, up from $3.8 million under current law.

Another Democrat of Manhattan, Council Member Bill Perkins, who is the lead sponsor of the bill, denied the measure was aimed at Mr. Bloomberg.

“Maybe the mayor’s spending has been the most egregious, but that is between himself and the mirror,” Mr. Perkins said. “The mayor is not going to be the mayor forever. This is about leveling the playing field for all candidates.”

Council Member Madeline Provenzano, a Democrat of the Bronx and the one committee member who voted against the bill, called the $6-$1 ratio “obscene” and said ramming it through for the 2005 election was “disgraceful.”

“A responsible legislative body would not let this take effect until a least one election cycle had intervened,” she said during the hearing.

Others on the committee echoed her concerns about how quickly it would be implemented, but ultimately voted for the bill, describing it as the only way to allow candidates running grassroots campaigns to compete.

“Anybody should be able to buy a yacht, three, four, five homes,” Council Member Michael Nelson of Brooklyn, said, “but not to buy an election.”

Council Member Philip Reed, a Democrat of Manhattan, ticked off his concerns but said: “It’s a small price to pay to try to minimize potential damage that these billionaires that come through here every once in a while running for office can inflict on the public.”

The bill was originally proposed with an $8-$1 maximum match, but that met widespread opposition. In addition to changing the formula, the bill adds more stringent financial-disclosure requirements for all candidates, including those, like Mr. Bloomberg, who bankroll their own campaigns; reduces city financing in noncompetitive races; restricts how incumbents can use government resources during an election year, and limits individual campaign contributions to $4,950.

The mayor’s communication director, William Cunningham, said that while self- financed candidates may spend more, they do not spend taxpayer money.