The Australian government's proposal to hold a national vote on legalising same-sex marriage has been defeated in the upper house of parliament.

The government said a non-binding ballot, or plebiscite, was the quickest way to amend the Marriage Act.

Same-sex couples can have civil unions or registered relationships in most Australian states but they are not considered married under national law.

Opinion polls indicate that most Australians support same-sex marriage.

However opposition parties and many supporters of same-sex marriage argued a plebiscite would be expensive and could unleash a divisive campaign.

Instead, they say parliament should make the decision itself.

The proposal's defeat in the senate means the issue will be taken off the agenda at least until the next term of parliament.

Marriage equality has proved a tricky issue for Prime Minister Malcolm Turnbull. He is personally in favour of same-sex marriage but is reluctant to allow his own MPs a free vote on the issue.

Labor Senator Penny Wong told parliament that, after much soul-searching, she had decided to oppose the plebiscite.

"We do not want our families and our children publicly denigrated," she said.

"This hate speech is not abstract, it is real, it is part of our daily life."

Greens Senator Janet Rice spoke about the challenges of her 30-year marriage to transgender woman Penny.

"We know that our same-sex marriage is just as important and valid and deep and wonderful and loving as our heterosexual one was," she said.

"People's human rights should not be subject to a popular vote."

Attorney-General George Brandis accused the Labor Party of "playing politics with gay people's lives".

"A vote against this bill is a vote against marriage equality," Senator Brandis told parliament.

"Those who claim to believe in marriage equality, but nevertheless, for their own cynical, game-playing reasons, are determined to vote against it, should hang their heads in shame."

Labor announced last month that it would not support the bill, condemning it to fail in the senate this week.

The move was celebrated by same-sex marriage supporters who widely favour the issue being voted on by parliament, without the need to put it to the public.

(BBC)