Immigration Minister Peter Dutton says he and other conservative colleagues are working to find a "sensible" way forward to resolve the issue of same-sex marriage in this term of Parliament.
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In an interview on Thursday, Mr Dutton confirmed a Fairfax Media report he was pushing for a postal vote plebiscite as a way to progress the issue without breaking the Coalition's election commitments.
Treasurer Scott Morrison and Finance Minister Mathias Cormann have also privately backed the postal vote idea.
"Lots of us are working together to find a sensible approach through this Parliament," Mr Dutton told 2GB radio.
He pointed to a postal vote on same-sex marriage, which would not require legislation to enact, as one option to resolve the issue.
"We've got to deal with the reality of the Senate - the Senate knocked back the plebiscite," he said.
Mr Dutton, who opposes same-sex marriage, said the government should maintain its election promise to hold a national vote on the issue before a vote in Parliament.
"We went to the last election with a policy saying that we support the current definition of marriage and that if there was to be a change we would need to go to a plebiscite," he said.
"The plebiscite was a very clear and deliberate proposal within our election promise and we shouldn't break that promise.
"I don't support walking away from our election pledge."
Liberal Party moderates and same-sex marriage advocates are concerned that a postal vote could work to the advantage of opponents of marriage equality.
They fear a non-compulsory vote would depress turn-out among Australians who support same-sex marriage but are not passionate about the issue.
Young Australians, who overwhelmingly support same-sex marriage, would also be less likely to vote by post.
Alex Greenwich, the chair of Australian Marriage Equality, said the proposal was a "desperate ploy" that would be a "pretty sneaky and underhanded way" to finalise the issue.
Gay rights advocate Rodney Croome said a postal vote plebiscite would be "inherently rigged" because the government - rather than the Parliament - would have total control over the process.
Liberal MP Trent Zimmerman, who is gay, this week publicly called for his party to hold a free vote on the issue.
He said the government had done its best to comply with its election commitments and the issue would drag on until the next election unless it is resolved.
Opposition Leader Bill Shorten said same-sex marriage should be resolved by a free vote in Parliament.
"I think Australians can't understand why this place can't do its day job," he said.
"Just have a vote on marriage equality.
"A postal vote, which is non-binding - it is an opinion poll. They should just have an opinion poll, which we have already had, and just let Parliament vote on it."
He said he was heartened by Coalition MPs such as Mr Zimmerman speaking out to advocate a free vote.
