Labour is committed to "undoing the damage" of the lobbying act, according to Angela Eagle, shadow leader of the House of Commons.
Eagle, the MP for Wallasey, was responding to a call from Sir Stephen Bubb, chief executive of Acevo, for the three main parties to include in their election manifestos a pledge to repeal part 2 of the act, which contains the sections that charities are most concerned about.
Eagle stopped short of saying whether a Labour government would repeal part 2 of the Transparency of Lobbying, Non-party Campaigning and Trade Union Administration Act 2014 and said that the party wanted to hear more from charities about the new laws.
"The government’s gagging law threatens democratic debate in this country," she said. "Labour is committed to undoing the damage it will cause, but wants to hear from charities and campaigners about how we can ensure we have fair elections with vibrant debate."
The act gained royal assent last month despite voluntary sector concerns that the legislation would significantly impair their ability to speak out on issues that could be regarded as party political in the run-up to elections.
Bubb last week wrote to David Cameron, Nick Clegg and Ed Miliband, the leaders of the three main political parties, saying charities must be open and transparent, but "we will not and should not accept that the government has the right to muzzle charities in this way and chill democracy".
In a statement, he said the act would exert a "sinister influence on the charity sector’s voice" and urged the three party leaders to stand up for charities and campaigning organisations by repealing the "unfair and unworkable" provisions of the act at the earliest opportunity.
A Cabinet Office spokesman said in response to Bubb’s letter: "As the legislation went through parliament, the government spoke to more than 50 organisations and made important changes to address the concerns raised while preserving the core purpose of the bill.
"In addition, the rules will be reviewed after the 2015 general election to make absolutely certain they are working in the way we intend. The government hopes Acevo and everyone with an interest in a transparent political system will work with us and the Electoral Commission to implement a revised system that works."
The Electoral Commission is expected to publish its guidance on the act by early July.