The City Council overrode a mayoral veto yesterday to increase public matching funds for candidates who face wealthy opponents in city elections.

The legislation, which is part of a package of laws on campaign finance, increases the cap on matching funds to $6 for every dollar raised, from the $5-to-$1 maximum now on the books.

The vote comes after months of head-butting between Mayor Bloomberg, who spent $74 million of his own fortune on his 2001 election, and the City Council, whose speaker, Gifford Miller, hopes to win Democratic nomination to challenge the mayor in next year’s election.

Mr. Miller and the bill’s lead sponsor, Council Member Bill Perkins, who may run for Manhattan borough president next year, both said yesterday the measure was needed because wealthy candidates who opt out of the program have an unfair advantage.

“Our campaign finance act has been correctly called the best municipal campaign finance system in the country,” Mr. Miller said. “Unfortunately, this is a system which is under attack.”

Mr. Bloomberg’s communications director, William Cunningham, shot back swiftly, saying the bill took direct aim at the mayor.

“Mark today as another fund-raising day for the City Council,” he told The Associated Press, “but it’s taxpayers who will pay.”

The council also overrode mayoral vetoes on related measures. Those bills require candidates who do not participate in the campaign finance program to disclose spending and fund raising, and limit contributions to $4,950 for individuals. Mr. Bloomberg has in the past said the $6-to-$1 match is an excessive use of taxpayer money.