UPDATE: New prime minister Malcolm Turnbull has confirmed he will stick with his party's policy of a people's vote on marriage equality.
Asked in question time on Tuesday about his past support for a free vote, Turnbull admitted that that is the more traditional route for reform of this nature, but that his party had settled on a policy.
"Our government, our party room has decided that the decision will be taken by a plebiscite," he said.
"At the next election, Australians will have a choice. The Labor Party will say vote for us and the marriage equality will be dealt with by the politicians in a free vote after the election. And we will say, if we are re-elected to government, every single Australian will have a say."
Advocates hope for action on marriage equality sooner rather than later, after Malcolm Turnbull successfully challenged incumbent prime minister Tony Abbott for the leadership of the Liberal party on Monday.
As the leadership spill unfolded in Canberra on Monday evening, speculation was rife about what the change might mean for marriage equality.
Abbott, who has long opposed same-sex marriage, was considered a roadblock to the reform as long as he was prime minister.
Under his prime ministership, a cross-party bill for marriage equality was introduced to the parliament by Liberal backbencher Warren Entsch and representatives from Labor, the Greens and independents.
However, hopes of a free vote on the bill for government MPs were quashed in August, when Abbott announced the Coalition would take a popular vote on marriage to the next election.
A source told BuzzFeed News on Monday night that Turnbull intended to stick with that policy. He has previously said that his preference would be for a plebiscite to be held at the next federal election.
Advocacy group Australian Marriage Equality has issued a statement hailing Turnbull's imminent ascension to the prime ministership as an "unprecedented opportunity" for reform.
"This is the first time in Australia's history that both the Prime Minister and Leader of the Opposition have supported marriage equality, giving us an unprecedented opportunity to achieve the reform," said Rodney Croome, national director of AME.
"We will seek an urgent meeting with Mr Turnbull to chart a way forward on a reform that he knows is important and urgent."
AME stepped forward to support a plebiscite after Abbott announced the government would take one to the next election. However, AME has maintained their support is in response to a political reality, and their preferred avenue of action would be a free vote in the parliament.
"My hope is that if there's a plebiscite it will be held at the next election to reduce cost and delay, and to give the next government a mandate to pass reform," AME spokesman Rodney Croome told BuzzFeed News.
"We would prefer this to be resolved by a vote in parliament but if there is a plebiscite we're ready for it. I have no doubt Australians would vote for marriage equality."
Lyle Shelton of the Australian Christian Lobby has urged Turnbull to stick with the government's existing plan of a plebiscite after the next election.
"Given that we now have a Prime Minister who supports changing the definition of marriage and therefore family, it is more important than ever for people who support Judeo-Christian values to engage with politics," Shelton said.
"This is not a time to be passive or silent about the things that matter for a flourishing society."
Shelton said he hoped Turnbull would "engage with the serious ethical issues" associated with marriage equality, citing commercial surrogacy and changing family structures as areas of concern.
"I hope Mr Turnbull will also consider how people whose views on marriage are deemed by the state to be bigoted will be allowed to exercise freedom of speech, conscience and religion," he said.