The Prime Minister has dashed hopes for a referendum to establish a new Indigenous advisory body, saying the idea is neither "desirable or capable of winning acceptance".

Key points: Government formally rejects the key recommendation of the Referendum Council

Government formally rejects the key recommendation of the Referendum Council New advisory body would "become seen as a third chamber of Parliament," PM says

New advisory body would "become seen as a third chamber of Parliament," PM says Government has taken a step backwards, Norther Land Council's spokesperson says

The decision has been met by anger among Indigenous people from across the country who endorsed the landmark Uluru Statement from the Heart.

The Uluru proposal was rejected at Cabinet five months on from the historic constitutional summit in Central Australia.

The Government has now formally rejected the key recommendation of the Referendum Council — a report it commissioned to consult widely with Indigenous people on constitutional change.

Malcolm Turnbull on Thursday said in a statement a new advisory body "would inevitably become seen as a third chamber of Parliament".

"Our democracy is built on the foundation of all Australian citizens having equal civic rights, all being able to vote for, stand for and serve in either of the two chambers of our national Parliament — the House of Representatives and the Senate," the statement said.

"A constitutionally enshrined additional representative assembly for which only Indigenous Australians could vote for or serve in is inconsistent with this fundamental principle."

Indigenous Health Minister Ken Wyatt denied the Government had been cowardly.

"It's a pragmatic level of thinking about the reality of what will fly with the Australian people and what won't," he said.

"That's a real kick in the guts for the Referendum Council and certainly a slap in the face of those proponents," shadow assistant minister Pat Dodson said.

Senator Dodson said he hoped the Uluru convention's other main proposal — for a treaties commission outside of the constitution — was not junked.

He pointed to reports earlier this decade that called for racial sections of the constitution to be removed, along with a statement acknowledging First Peoples.

Senator Dodson co-chaired an expert panel, which in 2012 suggested repealing a section that allows Parliament to make laws for racial groups, and scrapping another part that contemplates excluding specific races from voting.

Timing on Uluru anniversary 'unfortunate', Minister concedes

The Government's announcement it would reject the proposal came on the 32nd anniversary of Uluru being handed over to its traditional owners.

Indigenous Affair Minister Nigel Scullion said the timing was unfortunate and was only because information was leaked to the media.

He said Cabinet had no choice but to block the proposal.

"We know it would have absolutely zero chance of success ... the only other alternative would be death by process," Mr Scullion said.

"I don't need evidence ... we have done a lot of polling, not on this particular is matter, but on other matters.

"Evidence is a long string, I'm not going to point that we do or don't have. It's our instincts."

'Turnbull has broken our hearts'

Mr Turnbull said he would establish a joint parliamentary committee with the Opposition to examine alternative proposals for constitutional change to benefit Indigenous people.

But the Referendum Council's Noel Pearson described the decision as devastating for the Indigenous community.

"I think Malcolm Turnbull has broken the First Nations hearts of this country, expressed in the Uluru Statement from the Heart," Mr Pearson said.

"He accused John Howard of doing that in 1999 and he has done the same thing in relation to recognition of Indigenous Australians."

Victoria's Aboriginal Affairs Minister Natalie Hutchins said the Federal Government had turned its back on Aboriginal people.

"To have gone to the lengths of setting up an advisory council and then totally rejecting what has come forward, it just makes you wonder where their commitment to Aboriginal Australians is," she said.

Joe Morrison from the Northern Land Council said the Government had taken a step backwards.

"I think the Parliament's failed the nation in terms of providing the requisite level of leadership here, and I think Prime Minister Turnbull needs to explain himself," he said.

"The proposal that was created out of Uluru was ... a key part but there was also the truth and justice-telling. But they were also laying the foundations for the substantial changes to the constitution."

Josie Crawshaw, a child protection advocate and a delegate at Uluru, said she was deeply disappointed.

"While our children are languishing in the jails and our communities are poverty-stricken, they've just wasted 10 years of a conversation, and tens of millions of dollars, to shelve this," she said.

Rod Little, co-chairman of the National Congress of Australia's First Peoples, said: "Aboriginal and Torres Strait Islander people have been let down once again."