Work is progressing on the format of a plebiscite on same-sex marriage.
The coalition has promised that a re-elected Turnbull government would hold a national vote on whether to change the Marriage Act, but has yet to say what question would be posed and how the plebiscite would work.
"George Brandis is coming back with some work on that," Cabinet Secretary Arthur Sinodinos told Sky News on Wednesday.
Senator Sinodinos welcomed former prime minister Tony Abbott's recent comment that he would support the outcome of the vote whichever way it went.
Labor says the plebiscite, which has been estimated to cost $160 million, is a waste of time and money and the parliament should vote on it before the election, due in September.
The opposition will push for a parliamentary vote on same-sex marriage before the planned plebiscite.
Labor MP Terri Butler flagged the move on Wednesday, saying Australians did not want a $160 million plebiscite on the issue.
"If the Liberals and the Nationals are saying they are going to vote however they like after a plebiscite - well that sounds like a free vote to me," Ms Butler told reporters in Canberra.
Government whip Brett Whiteley said there were "bigger fish to fry" in terms of parliamentary priorities.
The plebiscite was the best way to find out the "heartbeat" of the issue.
"We're going to let every adult Australian have a vote," he told reporters.
Nationals senator Matt Canavan has added his name to conservatives promising to honour the decision of the Australian people, with the proviso any changes must not contravene human rights.
He has challenged same-sex marriage supporters including Labor's Penny Wong and Greens leader Richard Di Natale to also bind themselves to the outcome, arguing they should have to vote against changing the Marriage Act if a majority of people voted no.
Nationals senator John Williams believes men who marry each other will never be the same as a man and a woman.
"There will never be equality," he told parliament on Wednesday.
"They can't have children for a start."
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