Bamaga, Cape York: Tony Abbott has continued to suggest Australians could vote on two separate referendums if he wins the next election, one on same-sex marriage and one on constitutional recognition of Indigenous Australians.

Several of his own cabinet believe the case is overwhelming for Mr Abbott to embrace a plebiscite on marriage equality and proceed with a referendum on Indigenous recognition.

But the Prime Minister kept the two-referendum option alive when he faced the media during his week in remote Indigenous Australia on Wednesday, saying he believed the Australian people were "more than capable of considering different important issues at different times".

Advocates of a plebiscite on marriage equality say it would be much cheaper than a referendum and that the High Court has already ruled that Parliament has the power to legislate on the question.

There is also a risk that a referendum would reduce the prospects of a successful referendum on constitutional recognition of Indigenous Australians – an outcome Mr Abbott has said he will "sweat blood" to achieve.

"I do think it would be problematic holding a full-blown referendum on both the same-sex marriage issue as well as the Indigenous recognition issue," said constitutional lawyer Anne Twomey, professor of constitutional law at the University of Sydney Law School.

"It would undoubtedly be the case that there would be distractions from the constitutional recognition question if you were first having one into same-sex marriage," she said.

"It mightn't be such a problem if it happened the other way around, with the Indigenous recognition going first and all concentration on that."

Mr Abbott was asked if he was not persuaded by the arguments against a referendum on same-sex marriage by colleagues including Attorney-General George Brandis, who is with him at Bamaga in Cape York.

"I'll be taking a proposal to cabinet in the next couple of weeks and it will then go to the party room," he said. "The important thing is that it will go to the people. This will be a people's decision not a politician's decision."

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