The ruling conservative Liberal Party has promised to hold a plebiscite on the issue if it returns to power at this weekend's election.
But questions remain over whether the party would abide by a result in favour of same-sex marriage.
Meanwhile a video has emerged of Opposition Leader Bill Shorten praising the idea of a plebiscite.
Mr Shorten last week slammed the government's plan as a "platform for homophobia" and advocated a parliamentary vote to decide the issue.
But he told a Christian lobby forum in 2013 that he would rather let the public vote on same-sex marriage than leave the issue to MPs.
Prime Minister Malcolm Turnbull is tipped to hold power at the election on Saturday and is aiming to hold a public vote on same-sex marriage by the end of the year.
But the result of the vote would be non-binding and MPs would need to pass further legislation to make it law.
Two senior Australian ministers have refused to say if they would support same-sex marriage in parliament.
In an interview, Treasurer Scott Morrison refused six times to say how he would vote.
"My view is, if the plebiscite is carried nationally, then the legislation should pass," Mr Morrison told the Australian Broadcasting Corp.
"If the plebiscite is not carried, then I think that settles the matter."
The treasurer - an evangelical Christian who worships at a Pentecostal megachurch - refused to give a straight answer when challenged for "clarity" on the issue.
In a separate interview, Foreign Minister Julie Bishop echoed the treasurer's comments, refusing to be drawn on the "hypothetical" issue.
"I would take my electorate's view into account, but I would also take into account how the plebiscite played out across Australia because, for example, a referendum gets up if it is a majority of states, majority of people in the majority of states," she said.
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