The Federal Opposition says the plebiscite would have resulted in a harmful debate against the gay and lesbian community and want a direct vote in parliament.

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

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

Nineteen senators debated the bill at its second reading after it passed the lower house late last month.

Prime Minister Malcolm Turnbull is personally in favour of same-sex marriage but is reluctant to allow his 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.”

Attorney-General George Brandis accused the Labor Party of “playing politics with gay people’s lives”.

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

Australian Marriage Equality spokesman Alex Greenwich says his organisation won’t give up and will continue to lobby federal politicians for a parliamentary vote.

“On marriage equality, peoples’ hearts and minds do change, and their voting pattern changes,” the MP told ABC Radio on Tuesday.

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.