Australia’s parliament has rejected the government’s bid to hold a national vote on the legalization of same-sex marriage in the country.

On Monday, the upper house Senate in Australia voted 33 to 29 against the proposal to hold a plebiscite on the issue that had been initially scheduled for February next year.

This is while the Australian center-right coalition government, led by Prime Minister Malcolm Turnbull, voted in August to take the controversial issue to a national poll, warning that a defeat would delay same-sex marriage in the country for years.

The opposition has demanded a direct vote in the parliament.

The bill to allow same-sex marriage has been introduced by Australian Attorney General George Brandis.

In October, Australia’s Labor Party which wants same-sex marriages legalized by the parliament, vowed to block the plebiscite, saying, "This country does not have the right in a plebiscite to pass judgment on the marriages and relationships of some of our fellow Australians.”

"It is not what Australia is about. We could make marriage equality a reality today by having a free vote in the parliament and that is what should be done,” it further noted.

Same-sex marriage is supported by 61 percent of Australians, according to a Gallup poll in August.

In most Australian states, same-sex couples can have civil unions or register their relationships, but the government does not consider them married under national law.