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.
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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.
