Cabinet minister Malcolm Turnbull says he doesn't support putting same-sex marriage to a national vote, as the issue should be resolved by the parliament this year.
Prime Minister Tony Abbott has flagged the idea of a plebiscite if the coalition wins the next election.
"The reason I haven't advocated a plebiscite after the next election is that it will mean that this issue is a live issue all the way up to the next election and, indeed, at the next election," Mr Turnbull told reporters in Canberra on Wednesday.
Mr Turnbull said a free vote on the issue was "consistent with Liberal Party tradition".
"One of the attractions of a free vote is that it would have meant the matter would be resolved in this parliament, one way or another, in a couple of weeks," he said.
Letting the issue continue unresolved beyond the election would mean the coalition would have less time to talk about the economy, jobs and innovation.
"The more time I can talk about (these issues) ... the happier I'll be," Mr Turnbull said.
The prime minister had "expressed a disposition to having some form of public vote", but it was not firm policy.
"That is a policy as yet unformed but it will presumably have to go through the normal cabinet process before it is fleshed out," Mr Turnbull said.
