Prime Minister Tony Abbott has said the government will confirm its policy on a same-sex marriage vote in the next fortnight, in a dramatic reduction of the time frame for the Coalition's national vote debate.

Last week, after the Coalition met to discuss a free vote on same-sex marriage, Mr Abbott noted that while the party would keep binding MPs against the reform until the next federal election, due in 2016, it was working on a new position centring on a plebiscite or referendum.

"Going into the next election, we'll have more to say," he told reporters last Tuesday.

But on Monday, Mr Abbott said there were a "few loose ends to tie up and that will be dealt with in the next couple of weeks".

The condensed time frame came as Coalition frontbenchers continued to differ on what the government's policy should be, with a cabinet discussion on the issue expected on Monday evening.

It also came as a cross-party bill on same-sex marriage was introduced, theoretically giving Parliament the opportunity to legalise the reform without a national vote.

Coalition MP Warren Entsch introduced his same-sex marriage bill on Monday morning, speaking to a near-empty government side of the chamber.

Supporting Mr Entsch was co-sponsor Teresa Gambaro and fellow Queensland Coalition MP Wyatt Roy. But the most senior signs of support came from Education Minister Christopher Pyne and Communications Minister Malcolm Turnbull, who split with the Prime Minister last week on his approach to same-sex marriage.

Assistant Education Minister Simon Birmingham also came over from the Senate to listen to the introduction of the bill.

When introducing his bill - which would allow celebrants but not ministers of religion to marry gay couples - Mr Entsch said that he wanted to remove discrimination in Australian law.

"Being gay is something not to be ashamed of," he said.

In a media conference shortly after Mr Entsch introduced his bill, Mr Abbott said same-sex marriage would go to a national vote in the next term of Parliament. But other Coalition MPs suggest the vote should be held before or at the next election. Frontbenchers also disagree on whether a plebiscite or referendum (which changes the constitution) is needed.

Last week, Social Services Minister Scott Morrison was shot down by Attorney-General George Brandis for his advocacy of a referendum. On Monday, Mr Morrison was less clear on his position. When asked if he wanted a referendum or plebiscite, he replied: "My position on these issues is well known."

On Sky News, Mr Pyne was emphatic that there was no need for a constitution-changing vote.

Mr Entsch's bill, which was seconded by Labor MP Terri Butler and backed by the Greens and independents Andrew Wilkie and Cathy McGowan, will come before the powerful selection committee on Tuesday evening.

The committee will decide when the bill comes on for debate, with the result of its discussion known after question time on Wednesday.

While some MPs have suggested the private member's bill will now languish on the books, the Greens' Adam Bandt described this as a "myth".

"The last time Parliament had a bill co-sponsored by Labor, the Liberals, Greens and independents, it passed both houses and became law," he said, referring to the protection for firefighters bill that passed in 2011.

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