Prime Minister Malcolm Turnbull has poured cold water on a Liberal backbencher’s move to present a private member’s bill to allow a conscience vote on same-sex marriage.

“The government’s policy is very clear: we support a plebiscite where all Australians would be given a vote on the matter and that remains our policy,” he told reporters in Paris.

West Australian senator Dean Smith is working on a plan to end the “embarrassment” of the nation and legalise same-sex marriage through a conscience vote in Parliament, defying his own government’s policy of a plebiscite on the issue.

Senator Smith, who is gay, said his private member’s bill was well advanced and he intended taking it to the party room for discussion in the near future.

“The bill is important because it will allow the Liberal Party to revisit the issue of marriage once and for all before the next election,” Senator Smith told the Sunday Times.

Mr Turnbull said Senator Smith, who crossed the floor against the plebiscite vote, was entitled to raise the issue in the party room but government policy remained.

Only last month, the Prime Minister was forced to rule out a parliamentary vote, even though he was a supporter of same-sex marriage.

The Prime Minister remains committed to a plebiscite on same-sex marriage.

That followed a leaked audio of senior frontbencher Christopher Pyne telling supporters a policy change on marriage would come “sooner than everyone thinks” but later apologised for his “ill-chosen and unwise” remarks.

Labor supports a conscience vote, rejecting the government’s plebiscite proposal.

“A free vote is the fastest, least expensive, least harmful way to achieve marriage equality,” Opposition Leader Bill Shorten said on Sunday.

“Dean Smith agrees with Labor and I know deep down the Prime Minister agrees with Labor.”

He said achieving marriage equality would be a legacy Mr Turnbull could rightly be proud of.

However an Essential Research poll last week found while almost two-thirds of respondents support same-sex marriage, well over half believe there should be a national vote.

Senator Smith concedes the Coalition’s plebiscite position is clear, so people should not underestimate the challenge of securing a free vote on the issue.

But he said a Senate report into the government’s own draft marriage bill as part of its plebiscite proposal is the blueprint for his own bill and the “most likely pathway for success”.

His bill would allow exemptions for religious and other celebrants who did not want to perform a same-sex marriage ceremony.

Senator Smith’s endeavours were welcomed by marriage equality advocates and urged politicians to get on with their job.

“Marriage equality is about the dignity and status of hundreds of thousands of Australians, our family members, friends and work colleagues,” Australian Marriage Equality’s Alex Greenwich said in a statement.

Just.equal’s Rodney Croome congratulated Senator Smith but urged him to consult with the LGBTI community to ensure any proposed exemptions do not go further than the LGBTI community would accept.

-AAP