Prime Minister Malcolm Turnbull introduced legislation on Parliament on Wednesday on the first anniversary of him getting the job.

He replaced Tony Abbott, who proposed that the public decide the issue with a popular vote and avoid a bitter debate in Parliament.

Mr Turnbull wants the compulsory vote to be on February 11, but it will be non-binding and Parliament would ultimately decide whether the law would be changed.

He told Parliament that the reason marriage equality advocates opposed the vote was because they thought enough politicians already supported the reform for it to become law.

"They don't want to run the risk of the Australian people giving them the wrong answer," Mr Turnbull said.

"For our part, we put our faith in the Australian people and we know that their answer, whether it is 'yes' or 'no,' will be the right answer."

Most gay rights activists are against a vote, saying it should be decided in Parliament without the potential divisive public debate.

They fear that government plans to spend 15 million Australian dollars (£8.3 million) on publicising the cases for and against marriage equality would give legitimacy to bigoted and homophobic views.

Mr Turnbull is a marriage equality advocate who is the only serving prime minister to attend Sydney's Gay and Lesbian Mardi Gras.

His government does not have a majority in the Senate, and two minor parties that back same-sex marriage have said they will not support the public vote.

The government's only chance of a plebiscite is now the opposition Labor Party.

Labor leader Bill Shorten has argued that a public vote would "give the haters a chance to come out from underneath the rock and make life harder for" lesbian, gay, bisexual, transgender and intersex people.

But Mr Shorten, who backs marriage equality, has not ruled out supporting the plebiscite to avoid a stalemate in Parliament over the issue that could last until the next election in 2019.

Attorney-General George Brandis, who supports same-sex marriage, accused Mr Shorten of jeopardising the reform to score political points against Mr Turnbull.

"I'm sorry to say, so far Mr Shorten has been putting political game playing ahead of the merits of the issue," Mr Brandis told Australian Broadcasting Corporation.

Mr Turnbull opposed the plebiscite before striking a deal with hard-right party powerbrokers to become prime minister.

Mr Shorten has also shifted his position, telling religious leaders in 2013 that he was "completely relaxed about having some form of plebiscite" on same-sex marriage.