Liberals agitating for a free vote on same-sex marriage have stepped up their campaign, with a key moderate arguing the party has never denied its MPs a conscience vote granted to their Labor rivals.

Victorian MP Russell Broadbent yesterday said the Coalition should not be "afraid" of a conscience vote on same-sex marriage while senator Simon Birmingham said he would continue to fight in the partyroom for a free vote.

Tony Abbott this week declared there would be no conscience vote for the Coalition following the ALP national conference decision to do so.

The Opposition Leader originally said the partyroom would discuss the issue in February when the private member's bill on same-sex marriage was introduced in parliament by Labor MP Stephen Jones. But he now says the Coalition would simply reaffirm the position it held prior to the last election, that marriage is between a man and a woman.

His change of heart this week angered a number of senior frontbenchers, and Senator Birmingham said yesterday he would still push for the vote.

"I think it's important that the Liberal Party honours its historical tradition of always granting its members greater freedom than does the Labor Party," he told Sky News.

"In this case, that would mean at least meeting the Labor Party on a conscience vote and I'll certainly take my viewpoint to the partyroom."

Mr Broadbent said it was the first time that Coalition MPs had not been allowed a conscience vote on a "substantive issue" when their Labor counterparts were allowed a free vote.

The Australian understands a parliamentary library paper that states this fact has been widely circulated in Coalition circles and was cited in Monday's shadow cabinet meeting, at which seven of Mr Abbott's most senior colleagues questioned his stand.

It came as Julia Gillard rescheduled the dinner with three same-sex couples that activist organisation GetUp! won at a charity auction.

The dinner was initially delayed and the Prime Minister will now meet the couples in February, along with prominent gay rights lobbyist Australian Marriage Equality national convener Alex Greenwich.

Mr Greenwich said the group was looking forward to the meeting with Ms Gillard at The Lodge and presenting its case for same-sex marriage.

Source: The Australian