The Turnbull government will wait until the "dust settles" before deciding its next move towards marriage equality.

Labor, the Greens, the Nick Xenophon Team and independent Derryn Hinch voted down in the Senate on Monday night the coalition's bill to enable a plebiscite on same-sex marriage in February.

Labor leader Bill Shorten said Prime Minister Malcolm Turnbull had been "too weak" to kill off the national vote idea, first proposed by Tony Abbott last year under pressure from the coalition's right wing.

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

But the issue was not off the agenda and Labor would continue to campaign for a free parliamentary vote.

Cabinet minister Christopher Pyne accused Mr Shorten of putting politics ahead of marriage equality.

"He couldn't care less about same-sex marriage and he doesn't care less about the many couples around Australia who'd like to have the same legal status as my wife and I enjoy," he said.

It would be foolish to make a decision in the heat of the moment about what the next steps might be.

"The sensible thing to do is let the dust settle on this issue and get on with the rest of our agenda," Mr Pyne said.

"I will always support marriage equality, but unfortunately Bill Shorten has snuffed out the prospects of that in the short term."

Deputy Prime Minister Barnaby Joyce said it was time to move on to other issues after the government's election mandate was rejected.

"People in the Senate know full well the promise that was made to the Australian people and the alternate promise that was made by Mr Shorten," he told reporters.

"The coalition won and, if nothing else, you should respect the will of the Australian people."

Australian Marriage Equality spokesman Alex Greenwich said his organisation would continue to lobby federal politicians for a parliamentary vote.

"On marriage equality, people's hearts and minds do change and their voting pattern changes," the independent NSW MP told ABC radio.

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

Gay Liberal backbencher Dean Smith was absent from the upper house for the final vote after earlier speaking out against a plebiscite.

He had argued a plebiscite was an abdication of parliament's responsibility and would undermine its sovereignty.

Independent senator Jacqui Lambie said those opposed to the plebiscite had "killed off people power".

She is talking with One Nation leader Pauline Hanson about putting legislation to parliament to hold plebiscites on same-sex marriage, indigenous recognition and euthanasia at the next federal election, likely to be in 2019.