Finding policy agreement on the issue is a test of prime Minister Malcolm Turnbull's authority over his government, which has trailed the center-left opposition Labor Party for months in opinion polls.
The conservative Liberal Party-led coalition was narrowly re-elected at elections in July last year with a promise to let voters decide whether Australia should recognize same-sex marriage through a popular vote. But the Senate would not allow the so-called plebiscite, which would have cost 160 million Australian dollars ($127 million) and the result could have been ignored by lawmakers when deciding how to vote on gay marriage legislation in the Parliament.
Liberal Sen. Dean Smith, a gay man who opposed legalizing same-sex marriage when he was appointed to the Senate in 2012, has drafted a bill to allow gay marriage now and wants his fellow Liberal lawmakers to be allowed to vote on it according to their consciences rather than to according to party policy.
"It's time for the party to put the matter to rest once and for all," Smith told reporters on Monday. Gay marriage opponents, including former Prime Minister Tony Abbott who initiated the plebiscite policy two year ago, argue that the government must stick to its election promise that marriage law would not be changed without a national vote.
"The last thing Australia needs is government by opinion poll," Abbott wrote in The Australian newspaper. "But neither do we need political parties that believe one thing one minute and the opposite the next," he added.
Other lawmakers have proposed a postal plebiscite in which voters mailed in their opinions instead of using ballot boxes as a cheaper option that would not need the Senate to approve the expense. Opponents argue that the postal option would also need Senate approval and have warned of a court challenge.
Gay marriage campaigner Anna Brown said her advocacy group The Equality Campaign would seek a High Court injunction to prevent any postal plebiscite. "The government needs to think very carefully before it expends up to AU$100 million of taxpayer dollars when it could resolve this issue in Parliament as soon as this week," Brown said.
Smith's supporters could present his gay marriage bill to Parliament this week, regardless of his party's policy decision on Monday. Turnbull's coalition has a single-seat majority in the House of Representatives, where the political leader who controls a majority becomes prime minister.
So a few lawmakers deserting the ruling party on gay marriage could leave the government powerless to block the bill. Liberal lawmaker Eric Abetz, who opposes gay marriage, said that would be a "grave matter" that showed the government had lost control of its legislative priorities.
Opinion polls show most Australians support gay marriage. But most of that support is soft, and gay-rights advocates are concerned that referendums rarely change the status quo in Australia. Turnbull supports gay marriage and initially opposed the plebiscite concept. But he agreed to maintain the government's plebiscite policy in a deal with the most conservative lawmakers in his party when he replaced Abbott as prime minister in September 2015 due to Abbott's poor opinion polling.