SYDNEY (Reuters) - Australia’s high court on Tuesday began a hearing on the validity of a government plan for a postal vote to legalize same-sex marriage, a challenge that risks destabilizing the ruling center-right coalition.

Pedestrians walk past banners set up by the City of Sydney promoting the "yes" vote for gay marriage in Australia, in Sydney, Australia, September 1, 2017. REUTERS/Jason Reed

If the court rules against the plan, Prime Minister Malcolm Turnbull could find himself presiding over a government fractured on the issue, endangering his razor-thin parliamentary majority of one.

With the non-compulsory vote a couple of weeks away, its opponents have launched a legal challenge, saying the vote needs the backing of parliament - which has twice rejected such a national ballot.

“This case is about dignity and equality for lesbian, gay, bisexual, transgender and intersex Australians,” Anna Brown, director of legal advocacy at the Human Rights Law Centre, which leads the opposition to the vote, told reporters in Melbourne.

“We’re here because we all believe and want marriage equality. This postal plebiscite has big question marks around its legal validity.”

Conservative lawmakers have threatened to resign if the ballot policy is not adhered to, risking Turnbull’s parliamentary majority.

But he may not be able to stick to the postal vote policy, as a group of liberal politicians has threatened to rebel and side with the opposition, which would probably end his tenure as leader, analysts say.

Turnbull supports same-sex marriage, as do two-thirds of Australians, but his party’s conservative wing has threatened a revolt if he deviates from the policy of a national ballot.

Frustrated by the political impasse, a group of backbenchers this year said they were ready to vote with the opposition Labor Party to secure same-sex marriage, a plan only abandoned when Turnbull offered a postal vote.

While a rejection of the legal challenge offers a political solution, an increasingly vitriolic campaign forced Turnbull to urge both sides to show mutual respect.

Turnbull’s plea has gone largely unheeded, however.

Opponents of same-sex marriage last week launched a contentious campaign advertisement that the government immediately rejected as inaccurate.

Since the postal vote is not a formal election it is not subject to the same rules on political advertisements, and activists fear a surge in malicious campaigning in the run-up.

“Our concern is around a sustained, intense campaign. It will make a question that should be a private matter between two people, a matter for public discussion,” Elaine Pearson, director of New York-based Human Rights Watch, who supports same-sex marriage but opposes the national vote, told Reuters.