Senior Government conservative Peter Dutton has called for a national postal vote on whether to legalise same-sex marriage.

Key points: Plan for $180m in-person same-sex marriage ballot was thwarted by Senate

Plan for $180m in-person same-sex marriage ballot was thwarted by Senate Peter Dutton said Government would be bound by the result of the vote

Peter Dutton said Government would be bound by the result of the vote Labor says plebiscite is policy of Government without "the courage to do what is right"

The Coalition is adamant there will not be a vote in Parliament on the issue until a plebiscite is held.

Its plan for a $180 million in-person same-sex marriage ballot was thwarted by senators from Labor, Greens and the Nick Xenophon Team last year.

Mr Dutton said there was momentum to settle the issue "one way or the other" before the next election.

"The plebiscite proper can't get through the Senate," he told Sky News.

"From that point, what's the next best option? In my mind it is a postal plebiscite, which allows the public to have their say.

"There's no doubt in my mind that a postal plebiscite delivers the same policy intent as a plebiscite proper."

This month's Queensland Liberal National Party convention passed a motion supporting a non-compulsory postal ballot.

Government bound by vote outcome: Dutton

Proponents argue a postal plebiscite could proceed without Parliament's support — in contrast to an in-person vote — and would be also cheaper.

A Senate Committee hearing earlier this year was told the Government had sought official advice about a postal plebiscite on same-sex marriage.

"If the majority of the Australian people have their say in favour of change, my view is that having advanced a democratic process — as a plebiscite is, or a postal plebiscite is — then the Government of the day is bound by that outcome," Mr Dutton said.

"I think that is a much cleaner process than people running off to support private member's motions or a Labor stunt within the House of Representatives."

Openly gay West Australian Liberal senator Dean Smith is drafting a private member's bill to allow same-sex marriage.

If Senator Smith's proposal was debated in the Liberal party room, MPs and senators could vote to overturn the plebiscite policy.

Labor leader Bill Shorten on Twitter rejected the postal vote idea, saying: "The postal plebiscite is a policy for a government that has neither the intellect to know what to do, nor the courage to do what is right."

A plebiscite on the matter was first proposed by former prime minister Tony Abbott and taken by his successor Malcolm Turnbull to the 2016 federal election.