Supporters of same-sex marriage rights in Australia have vowed to continue fighting after the parliament's upper house ditched a proposed February plebiscite on recognizing gay marriage.

The Australian senate on Monday night voted down the conservative government's bill to hold a public vote by a margin of 33 to 29.

Leader of the opposition Labor party, Bill Shorten, said Tuesday he will not apologise for blocking the bill. The government needed Labor's votes to pass the bill to hold the plebiscite on same-sex marriage.

"Labor makes no apologies for helping to block the plebiscite - the LGBTI community didn't want it, and the Australian community didn't either," he told reporters on Tuesday.

Shorten criticized Prime Minister Malcolm Turnbull for being "too weak" to kill off the plebiscite due to pressure from his right-wing colleagues. He called for a free parliamentary vote on the same-sex marriage legislation without going to the public.

Australian Marriage Equality spokesman Alex Greenwich also said his organisation would lobby the federal politicians to hold a vote on same-sex marriage in parliament instead.

"We are closer than ever before to achieving marriage equality ... The path ahead is clear and direct and remains what it has always been, a vote in parliament by our elected representatives," said Greenwich, a state parliamentarian for the New South Wales.

The plebiscite plan was supported by same-sex marriage opponents, while most of the gay marriage advocates had opposed it, since, they argued, it would spark a hateful and divisive public debate.

Several gay senators, including Labor's Penny Wong and Louise Pratt, made an impassioned pleas against the plebiscite, saying the vote would denigrate their families and subject them to hate speech.

Dean Smith, a popular gay senator from Turnbull's party, abstained from the vote. He was against the plebiscite.

The government has not said how it intends to take the issue forward, but deputy prime minister, Barnaby Joyce, said on Tuesday the country should move on to other issues since the bill was voted down.