Senior Liberal Peter Dutton has pushed the case for a postal plebiscite on the issue of same sex marriage, saying he would like it resolved in this term of parliament.
He says a postal plebiscite would require no legislation but would deliver the same policy intent as a proper plebiscite, which has been blocked by the Senate.
"I think that is a much a cleaner process than people running off to support private member's motions or a Labor stunt within the House of Representatives," Mr Dutton told Sky News on Sunday.
Labor, the Greens and others have rejected the idea of plebiscite, instead they believe there should be a free vote in the parliament.
Earlier, this month Liberal senator Dean Smith confirmed he was drafting a private members' bill to take to the Liberal party room in the coming months for a conscience vote.
Mr Dutton said there was momentum in relation to having the matter resolved one way or the other.
"The next best option in my mind is a postal plebiscite which allows the public to have their say," he said.
He said if a majority of the Australian people favoured a change in the definition of marriage, then the government of the day would be bound by the outcome and legislation would come before the parliament.
Opposition Leader Bill Shorten slammed the proposal.
"The postal plebiscite is a policy for a government that has neither the intellect to know what to do, nor the courage to do what is right," he tweeted on Sunday.