Tackling a highly charged topic that is likely to affect the 2013 race for mayor, the New York City Campaign Finance Board wrestled on Thursday with the contours of a new law requiring more disclosure of campaign spending by independent groups like unions and corporations.

The board, which held a public hearing, is not expected to formulate specific rules for at least a month. But given the board’s concerns, as spelled out in a briefing paper, over an “unprecedented level of third-party activity” in the 2009 municipal elections, the new law is likely to curtail the influence of the city’s powerful labor unions in virtually every contest from mayor to City Council.

A ballot initiative calling for tighter campaign finance controls was approved by 84 percent of the vote in November, but it is up to the board to devise specific rules to administer the law, which was also a response to the decision by the Supreme Court last year allowing corporations and unions to spend an unlimited amount of money in candidate elections.

The effort to codify the ballot initiative comes at a difficult time for the labor movement, which has been on the defensive both nationally and locally over collective bargaining rights, pension and health care benefits, proposed job cuts and other issues.