Prime Minister Malcolm Turnbull refuses to endorse same-sex marriage pledge

Speaking on Sky News on Sunday, Senator Brandis said the government would hold a plebiscite on same sex marriage before the end of the year if it won the federal election expected late this year.

And if there was support for it, Senator Brandis said,the Coalition government would quickly introduce changes to the Marriage Act that he expected would become law "by the end of the year".

Mr Turnbull's office, however, distanced itself from Brandis' comments that a plebiscite would be held by the end of the year.

A spokeswoman for Mr Turnbull said only that the government was committed to holding the plebiscite "as soon after the election as can be done".

Labor leader Bill Shorten said the comments showed the government's "chaos and division" had reached new heights.

"This is a new land speed record for a broken promise – made over breakfast and gone before dinner," he said.

The Australian Electoral Commission last year warned a public vote on same-sex marriage should not be rushed.

And if an election is held in October, as Mr Turnbull has suggested in previous statements, it is difficult to see how Senator Brandis' timetable could be met.

In verbal evidence to a Senate inquiry last year into a popular vote on marriage laws, Australian Electoral Commissioner Tom Rogers said three months would be required to organise a public vote

In a written submission, the commission said if a same-sex marriage referendum were to be held in conjunction with a federal election it would need 29 weeks to prepare.

Whether running a joint, postal or stand-alone vote, the commission said it would need "adequate lead time to procure materials" and that rushing such a vote "carried certain risks".

However, Mr Rogers told the inquiry the AEC was at the service of the government, so it would run an electoral event in any timeframe it was given.

The policy confusion came just hours after Mr Turnbull attended the Sydney Gay and Lesbian Mardi Gras on Saturday night, the first sitting prime minister to do so.

Mr Shorten and deputy leader Tanya Plibersek marched in the annual parade.

Labor accused Mr Turnbull of failing to stand up to his party's "rabid" conservatives by pursuing the plebiscite, which would cost an estimated $160 million, rather than pursue a change in legislation.

"The majority of Australians support same-sex marriage and want it legislated without delay, Mr Shorten said.

In Sunday's interview Senator Brandis said both he and Mr Turnbull wanted to allow same-sex marriage.

He said the Coalition would propose during the election campaign that relevant sections of the Marriage Act, which contain the current definition of marriage as being between a man and a woman – inserted by the Howard government – should be amended.

Senator Brandis said this was not a response to Labor's policy – which is to hold a parliamentary vote on same sex marriage within the first 100 days of a Shorten Labor government – but a question of doing what is right for the country.

"I believe that marriage is one of the fundamental institutions of society and I think it's important that the fundamental institutions of society reflect the fundamental values of society," Senator Brandis said.

"We will be going to the election promising a plebiscite before the end of the year," he said.

In the event of a "yes" vote, Senator Brandis said, "I would it expect it to be legislated by the end of this year."

Senator Brandis said he understood why conservative electorates around the country, might choose to vote no in a plebiscite.

But he also believed there was "virtually no doubt at all" that if the public votes "yes" to same-sex marriage, then the Parliament "will follow".

Australian Marriage Equality national director Rodney Croome said government should enact marriage equality immediately rather than put the matter to a plebiscite.

If a plebiscite was held, the result should automatically become law rather than "return to parliament for further debate and delays", he said.

"If the government allowed a free vote in Parliament we could have marriage equality next week rather than delaying until the end of the year," Mr Croome said.

If same-sex marriage became legal, Australia would join countries such as Canada, the United Kingdom, United States, France, New Zealand, Ireland and South Africa, which have already legalised it.