Tony Abbott won't say whether he supports a plebiscite or a referendum on same-sex marriage but he believes a national vote should be kept separate from next year's federal election.
The prime minister says millions of people have strong views on the issue.
"Why shouldn't we be able to debate this and decide this in its own right without being distracted by the sorts of arguments which you inevitably get during an election campaign?" Mr Abbott asked reporters in Brisbane on Sunday.
The cabinet will meet on Monday, its first gathering since the coalition joint party room voted not to have a conscience vote on gay marriage, instead leaving the decision to the people.
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Attorney-General George Brandis is unsure whether the meeting will determine how this should be done.
"But I do expect that this is a decision the government should make very soon," he told Sky News on Sunday.
However, Senator Brandis is at odds with the prime minister, saying a compulsory-voting plebiscite could be held on the same day as an election, saving taxpayers millions of dollars as opposed to being held separately.
He also disagrees with holding a referendum, put forward by fellow cabinet ministers Joe Hockey and Scott Morrison, because he says the constitution already enables parliament to legislate for same-sex marriage, should it choose to do so.
"So the right way to test public opinion on this issue, given that it doesn't raise a constitutional question, is to have a plebiscite," he said.
Liberal backbencher Warren Entsch is still expected to introduce his same-sex marriage bill, seconded by Labor, into parliament on Monday, but it is not expected to be voted on.
Mr Abbott said a "very strong disposition" emerged from the party room that the issue was best decided by the people, not by politicians.
Deputy Labor Leader Tanya Plibersek believes Mr Entsch's bill should go to a vote.
"People will have a choice at the next election. They can go down this expensive delaying path that Tony Abbott's proposing or support Labor and have marriage equality in the first 100 days (of government)," she told Nine Network.
Victorian Greens senator Janet Rice said the government was just putting "hurdle after hurdle and roadblock" in the way of marriage equality.
"If we had our politicians actually listening to the community and had a free and fair vote in the parliament, well then a vote would succeed," she told ABC television.
Meanwhile, Liberal MP Andrew Laming has been criticised for the way he conducted a gay marriage survey of his electorate, which concluded 58 per cent of residents were opposed.
The Brisbane-based MP had promised to follow the wishes of his electorate, in the event the Liberal Party granted a conscience vote on the issue.
Marriage equality campaigners say Dr Laming's survey was only available through the post and wasn't online.
"The paper copy was not received by large swathes of the electorate," advocate Adele Fisher said in a statement.
