Australians will be asked to vote on same-sex marriage through a postal plebiscite, the Turnbull government has confirmed, provided the Senate once again knocks back its plan for a compulsory national poll.

The Liberal Party agreed on the new policy on Monday night during a two-hour emergency meeting, rejecting a push from five Liberal MPs who demanded a free parliamentary vote on the issue.

It is unclear whether those MPs will now join with Labor and the crossbench to back a free vote – an outcome most observers say would result in same-sex marriage becoming legal.

Speaking after the specially-convened meeting, Acting Special Minister of State Mathias Cormann said the government hoped to re-introduce the plebiscite legislation to the Senate this week.

“If that were to fail, the government believes that we have a legal and constitutional way forward to give the Australian people a say … through a non-legislated, voluntary postal plebiscite,” he said.

If Australians voted in favour of same-sex marriage, Senator Cormann said the government would allow a free vote on the issue in the Parliament.

“Our expectation would be that that law would pass the Parliament,” he said.

It was not clear if the government would grant a free vote on the issue if the postal plebiscite failed.

Same-sex marriage advocates hope Parliament will act this week.

The compulsory plebiscite legislation is almost certain to be rejected by the Parliament again, with key crossbenchers Nick Xenophon and Derryn Hinch saying on Monday night they would once again vote against it.

But the government is attempting to pressure them to change their mind, with Senator Cormann saying it was up to the Senate to decide whether they prefer the compulsory attendance plebiscite or voluntary postal vote.

“If there are concerns about a voluntary postal plebiscite, then I would encourage those senators who are so concerned to consider supporting the government’s bill for a compulsory attendance plebiscite,” he said.

The move also will guarantee a legal fight between the government and same-sex marriage advocates, who warned that if a postal vote was announced, “the challenge will begin against it tomorrow”.

Advocates, who were present in Canberra to lobby Liberal politicians ahead of the emergency party room meeting, released legal advice on Monday suggesting a postal vote would be blocked by the courts.

They argue the postal vote would require legislation to enact, but the government believes it can direct the Australian Electoral Commission to carry out the poll without the approval of Parliament.

“Today the government has broken the hearts of gay and lesbian people across Australia,” Equality campaign co-chair Anna Brown said.

The government also said it has legal advice backing the postal plebiscite, though Senator Cormann indicated it would not be made public.

Opposition Leader Bill Shorten criticised the government’s paralysis over marriage in a speech to the Labor caucus on Monday.

“There is only one reason why this failure to deal with marriage equality has dragged on as long as it has, it is because of the complete failure of leadership and weakness of the Prime Minister of Australia to deal with this issue,” he said.

During Monday’s Liberal Party meeting, Dean Smith, Tim Wilson, Trent Zimmerman, Trevor Evans and Warren Enstch were among those who pushed for a free vote, but a clear majority of Liberal MPs backed the government’s existing policy for a plebiscite.

The postal vote option must be approved by the Coalition’s joint party room meeting – which also includes Nationals MPs – on Tuesday.