After failing in its previous attempt, the City Council is giving campaign finance reform another go.

Yesterday, its Government Operations Committee held a hearing on a proposal that would increase the cap on matching funds for candidates running for public office.

Designed to even the playing field for candidates facing wealthy opponents who bankroll their own campaigns, the proposal would boost matching funds to a maximum of $6 for every dollar raised, from the $5-to-$1 cap now on the books.

The committee chairman and lead sponsor of the bill, William Perkins, a Democrat of Manhattan, said the proposal would temper the widespread opposition to an earlier $8-to-$1 proposal, criticized as being too generous with public money.

In addition to the change regarding matching funds, the legislation would stiffen disclosure requirements for all candidates and make subject to city campaign rules war chest money that candidates hold over from other public offices.

“You can’t stop a Bloomberg with any bill, because he’s worth $5 billion and no matter how high we go, he can go higher,” said Mr. Perkins. “The purpose of this bill is to say to those who play by the rules, ‘Look, we are not going to let the bully get away with it. If we can’t stop the bully, then we’ll make you bigger.'”

Mayor Bloomberg, who spent $75 million of his own money on his 2001 campaign, has criticized the council’s past attempts at reform, characterizing them as a transparent manipulation aimed at the upcoming mayoral election, in which Council Speaker Gifford Miller plans to run.

“The city’s got lots of things to do with its money and, given that you’ve got virtually no turnover in incumbents, it’s pretty hard to argue that incumbents need that kind of subsidy from the taxpayer to run,” Mr. Bloomberg said yesterday about the new proposal.

“There are lots of people that run for these offices – like for the office of mayor,” he added. “That would give you, would indicate, that money isn’t the issue.”

Under current law, candidates who participate in the city-subsidized system are eligible for a $4-to-$1 matching rate at the outset and $5-to-$1 when their opponents spends half the designated expenditure cap.

The Perkins legislation would add a third tier, increasing matching funds by another dollar for candidates with opponents who spend double the limit. In the mayoral race, for example, a candidate running against someone who spends twice the $5.7 million cap becomes eligible for the $6 rate.

The bill would also reduce by 25% the money the city puts up for candidates in noncompetitive races and prohibit government-financed mass mailings for the last three months before an election, versus the current one month.

The chairman of the city’s Campaign Finance Board, Frederick Schwartz, testified that he generally supports the bill, but said he was unsatisfied with some provisions, including regarding the war chest transfers, which he wants eliminated entirely.

Representatives from Common Cause New York and the Citizens Union said they were pleased the council was moving to reduce monetary barriers that prevent grassroots candidate from running, but said they support even stronger provisions and questioned why the effort was taking place was so close to the election.