If either from of the public vote takes place, Australia's Parliament would then decide whether to adopt a new law allowing same-sex couples to marry.
Same sex marriage will be considered again by the joint party room meeting in Canberra on Tuesday, and will continue to play out as a divisive issue for much of the rest of the year.
SENATE to vote this week on legislation to run a compulsory plebiscite on November 25.
However, a spokeswoman for Acting Special Minister of State Mathias Cormann confirmed the original Bill - Plebiscite (Same-Sex Marriage) Bill 2016 - would be introduced in its current form.
Liberal MPs met for two hours last night, where they voted to put a plebiscite before Parliament for a second-time.
"I'll be voting yes, as will (my wife), I'm very open about that but the Australian people are never wrong when they vote, whether it's for governments or on matters like this, their vote will be respected", Turnbull said.
The Courier Mail has reported that marriage equality campaigners are bracing to launch a High Court challenge in the eventuality that a postal vote is undertaken, questioning the legality of this course of action without senate authorisation.
Bill Shorten criticised the postal vote during Question Time.
Rights advocates see the plebiscite as both a delaying tactic forced by a hard right-wing minority and a strategy to undermine political support.
"There are arguments against plebiscites, I understand that".
"They had the opportunity to resolve this matter and they said no, they said we are going to drag this out".
A postal plebiscite would have at least served as a circuit-breaker, despite the legal uncertainty that clouds the proposal. The government confirmed on Tuesday that the Australian Bureau of Statistics - you may remember them from such successful ventures as the #CensusFail - will be in charge of the votes.
Responses would be voluntary and therefore less indicative of public opinion. Turnbull's leadership would become untenable and he'd no longer be prime minister.
Turnbull said the legislation would be reintroduced again this week, and if rejected a voluntary national postal vote would be held instead without parliamentary approval.
The government has assured Australians living overseas they will be allowed to have their say.
Lyle Shelton, managing director of the Australian Christian Lobby, said his advocacy group had collected 55,000 signatures on a petition demanding a plebiscite.
Mr Shelton handed the petition to Senator Cory Bernardi, leader of the minor Australian Conservatives party, to present to the upper house.
Abbott and the social conservatives are competing with Senator Corey Bernardi's breakaway Australian Conservatives and Senator Pauline Hanson's One Nation in trying to mobilise religious forces.
Tasmanian crossbench senator Jacqui Lambie, who voted in favour of the plebscite last November, said she would not support a postal vote.