SYDNEY (Reuters) - Australia will hold a non-compulsory postal vote on legalizing same-sex marriage if a second bid to win political support for a national ballot fails, a minister said on Monday.

People walk across a rainbow pedestrian crossing painted on Sydney's Oxford street, the city's main gay district April 4, 2013. REUTERS/David Gray

The postal vote proposal offers a path for Prime Minister Malcolm Turnbull to retain the support of both liberals and conservatives in his center-right coalition, crucial given his one-vote majority in the lower house of parliament.

Same-sex marriage is supported by 61 percent of Australians, a 2016 Gallup opinion poll showed, but the issue has fractured the government and damaged Turnbull’s standing with voters.

Late last year, the upper house Senate rejected a government proposal on the matter, with opponents saying they believed it was best dealt with by a free vote in parliament.

On Monday, Finance Minister Mathias Cormann said the government would re-introduce the same legislation, but accompanied by a contingency plan to counter any rejection by the upper house, where the government does not have a majority.

“Our preference is to have a compulsory attendance plebiscite,” Cormann told reporters in Canberra, Australia’s capital.

“If that were to fail, the government believes that we have a legal and constitutional way forward that gives the Australian people a say on whether or not the definition of marriage should be changed.”

Legal experts said a postal vote may also require Senate approval, however, setting the scene for a likely court challenge to the government’s plan.

“The legal advice we have is that such a step, conducting a plebiscite, would be invalid,” Anna Brown, director of legal advocacy at the Human Rights Law Centre told reporters in Canberra.

“That’s why we’d go straight to the High Court and launch the challenge.”

Frustrated by the political impasse on the measure, a group of five backbenchers have said they would vote with the opposition Labor Party for a free vote.

In July, a government senator said he was drafting a private member’s bill aimed at legalizing same-sex marriage, but Turnbull said he would not allow the bill to be voted on.

It is unclear whether the postal vote proposal will be enough to keep rebel backbenchers from pushing ahead with their own legislation.

Resignation by any backbencher would force Turnbull into attempting to form a minority government. But he also cannot afford to lose the support of his conservative wing.