A joint parliamentary committee is urging politicians to ‘co-design’ an Indigenous advisory body to parliament as it revives hopes of constitutional recognition for First Nations peoples.

The Joint Select Committee on Constitutional Recognition for Aboriginal and Torres Strait Islander peoples delivered its final report on Thursday.

But, in what is likely to anger activists who want to speed up the process, it warns the concept "needs more work".

"It's a new concept in this debate and we want to get the detail right," said Liberal co-chair of the committee, Julian Leeser.

"I've never said it would represent a third chamber."

It is a distinct departure from the criticisms of Malcolm Turnbull and Scott Morrison of the Voice.

The report outlines a roadmap for a successful referendum to recognise Indigenous Australians in the Constitution, as well as the controversial advisory body which the last two Prime Ministers have rejected.

It comes after the landmark Uluru Statement from the Heart in May last year recommended an Indigenous ‘Voice to Parliament’.

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"The Voice to Parliament is still on the table. The referendum is still on the table. The truth-telling process is on the table," Indigenous Labor senator and committee co-chair Pat Dodson told SBS.

"I know people are sick of politicians' promises but the Labor party is very set and determined about this."

The Liberal members of the committee are also confident the proposal can become a reality.

"This is taking the Voice to the next step," Mr Leeser said.

"The Voice will succeed because it will be legitimately designed by Aboriginal and Torres Strait Islander peoples."

The major recommendations from the committee are to co-design the process for establishing the voice with Indigenous people, work with them to decide on the wording of constitutional recognition, encourage a truth-telling process; and establish a national tomb for unknown Indigenous remains.

"It's all designed with First Nations peoples to get things right," Senator Dodson said.

"The order of things may be where we differ a bit."

Mr Leeser said the Uluru Statement lacked detail, which led to the long-running Recognition campaign stalling.

"It needs more work," Mr Leeser said.

"It's a new concept in this debate and we want to get the detail right."

It is a distinct departure from the rejections of the Voice by Malcolm Turnbull and Prime Minister Scott Morrison.

The Liberal leaders had dismissed it as a third, unrepresentative, chamber of Parliament.

In September, Prime Minister Morrison said he supported reconciliation but rejected the proposal for a Voice to Parliament.

"People can dress it up any way they like but I think two chambers is enough," he told ABC radio.

Labor leader Bill Shorten has been unequivocal in his support for the Voice.

"I cannot be any more clear than this: Labor supports a voice for Aboriginal people in our Constitution, we support a declaration by all parliaments, we support a truth-telling commission," he told the Garma festival this year.

Senator Dodson said the referendum would take precedence over moves to turn Australia into a republic.

"That's another conversation that has to happen in Australia, but the time for it is probably not quite there."

While the Greens also supported the report's recommendations, the party urged Parliament to act quicker.

"Legislating the Voice before enshrining it in the Constitution is forcing First Nations peoples to audition and prove themselves," the party said.

"The Greens do not agree that the design of the Voice should be finalised prior to a referendum on the concept itself."