Social Services Minister Scott Morrison has suggested a full constitutional referendum on the question of how to define marriage.

Prime Minister Tony Abbott has argued his plan to put same-sex marriage to a vote would give the people a say, but he has not said how it would work.

Treasurer Joe Hockey said options included a plebiscite "where there is a question put to the Australian people".

He said a referendum was another alternative "to change the constitution, Section 51 (xxi), where it's defined as the Commonwealth having power over marriage".

Last night on the ABC's 7.30 program Mr Morrison suggested a full referendum.

"The type of issue that could be canvassed under Section 51 of the constitution — simply at the moment, in Clause 21, it just says 'marriage'," Mr Morrison said.

"You could equally put in there opposite- and same-sex marriage and clarify very clearly what the meaning of the constitution is on this question, and to reflect [what] some would argue has been a societal change since the constitution was first written."

Mr Morrison acknowledged the High Court had already ruled on it.

"Justices of the High Court have already expressed opinions on this issue, that's fine, but what I am saying is I would prefer the Australian people decide this: not me, not [High Court Chief Justice Robert French], but the Australian people."

Parliament should deal with same-sex marriage: Dreyfus

Shadow Attorney-General Mark Dreyfus dismissed that view.

"Scott Morrison is talking nonsense," he said.

Mr Dreyfus said the High Court handed down a decision in December 2013 in relation to the ACT's attempt to legislate on the subject.

"The High Court made it crystal clear that marriage is a matter for the Commonwealth Parliament to legislate on," he said.

"The constitution leaves no doubt on that subject, and as the High Court helpfully made clear in its decision, marriage has changed depending on how the Commonwealth Parliament has chosen to legislate about it at different times and it can change again."

Mr Abbott has said it could either be a plebiscite or a referendum, but in May, when Ireland held a referendum and voted in favour of allowing gay marriage, he rejected a suggestion Australia could take the same approach.

"Referendums are held in this country where there is a proposal to change the constitution," Mr Abbott said in May.

"I don't think anyone's suggesting that the constitution needs to be changed in this respect.

"Under the constitution, questions of marriage are the preserve of the Commonwealth Parliament; other matters of regulation of society are normally a matter for the state parliaments.

"Plainly, this is a matter that could quite properly come before the Commonwealth Parliament if members of Parliament wanted it to be raised."

Mr Dreyfus argued it was unnecessary because Parliament could deal with the issue, and said a referendum would come with a multi-million dollar price tag.

"It would cost probably in the order of $120 million of Australian taxpayers' money to hold this event," he told the ABC's AM program.

"The Australian Electoral Commission gave us that estimate when we were considering a referendum on recognition of local government back in 2013."