Government MPs who oppose same-sex marriage have argued the Coalition must maintain its policy for a national vote — saying it is "a plebiscite or nothing".

Key points: Senator Eric Abetz says party room and PM committed to plebiscite over parliamentary vote

Senator Eric Abetz says party room and PM committed to plebiscite over parliamentary vote Malcolm Turnbull did not rebuke Liberal senator for drafting a same-sex marriage bill

Malcolm Turnbull did not rebuke Liberal senator for drafting a same-sex marriage bill Gay marriage advocate says if free vote allowed "this will pass"

West Australian Liberal senator Dean Smith, who is gay, has confirmed he is drafting a bill to allow same-sex marriage and wants it voted on in Parliament by the end of the year.

But Tasmanian Liberal senator Eric Abetz, who is strongly against allowing same-sex marriage, insisted there should be a plebiscite, not a parliamentary vote.

But a plebiscite looks very unlikely to happen as the Senate last year blocked a bill to set up a national poll, and the Government has not tried again.

The Coalition is deeply split on the issue.

Senator Abetz argued the Coalition must maintain the policy it took to the last election and said Prime Minister Malcolm Turnbull had reiterated that the party's preference was for a plebiscite.

"That is the party room's strong view, that is something that the Prime Minister has restated very strongly in recent times," Senator Abetz said.

Privately, Coalition frontbenchers noted Mr Turnbull did not directly criticise Senator Smith when he was pressed on the development while in Paris.

"Dean crossed the floor against the plebiscite bill in the Senate, so he's got a longstanding view about it," Mr Turnbull said.

"In our party room members are allowed to raise whatever issues they like."

Same-sex marriage advocate Rodney Croome said it was a positive development.

"The Prime Minister seems OK with this path being forged … and the best thing the Prime Minister can do now I think is just step out of the way and allow his party room to decide if they will have a free vote or not," Mr Croome said.

"If they do decide to have a free vote … believe me this will pass, it'll take no more than a couple of hours and Australia can finally move on from a debate that has gone on for too long."

Parliament is due to sit again for two weeks from August 8.

Smith bill follows Pyne leak

In a leaked recording made public by News Corp last month, Liberal frontbencher Christopher Pyne suggested gay marriage would be legalised soon.

"Friends, we are in the winner's circle — but we have to deliver a couple of things and one of those things we've got to deliver before too long is marriage equality in this country," Mr Pyne said to a private Liberal party function.

"We're going to get it. I think it might even be sooner than everyone thinks.

"And your friends in Canberra are working on that outcome."

Former Prime Minister Tony Abbott suggested the comments showed Mr Pyne had been a disloyal member of this Cabinet. Mr Pyne later apologised for saying them.