Last weekend in remote northeast Arnhem Land, the powerful indigenous leader Galarrwuy Yunupingu opened the 21st Garma festival, Australia's largest Aboriginal festival attended by nearly 3000 people.

He had a warning for the PM, who's rejected a proposal for constitutionally enshrined "First Nations Voice" to parliament, while still promising to "progress" constitutional recognition for indigenous Australians.

This voice - a permanent, elected body that would advise on Aboriginal and Torres Strait Islander issues - was the key recommendation of the 2017 Uluru Statement from the Heart signed by indigenous leaders.

"This time we are saying enough is enough for the Yolngu people (of northeast Arnhem Land)," said Dr Yunupingu, the 71-year-old leader of the Gumatj clan of the Yolngu people on whose land Garma is held.

"There have been many times that we have gone to the government asking what they must do to help Aboriginal people - they haven't done it.

"If they don't come to us with an answer, we will tell you what we, the Yolngu people are going to do.

"We will dismiss the constitution, and [tell them] not to worry about us because we have thrown it out of Australia into the saltwater."

The fiery speech was delivered by the wheelchair-bound Dr Yunupingu while he was barely two metres from the new Indigenous Australians Minister and Noongar man Ken Wyatt, whom he asked to take his message to the absent prime minister.

Dr Yunupingu, who is understood to want even more change, such as possibly forming a Yolngu version of a parliament and laws, said the constitution "rejects the Yolngu people".

The next day, he announced he intended suing the Commonwealth and making a Native Title claim over the granting of leases for the former alumina refinery and current bauxite mine on his homelands.

That declaration comes more than 50 years after his father made history launching legal action to stop Swiss miner Nabalco building the mine in the first litigation on native title in Australia.

AAP understands a new claim could run into hundreds of millions of dollars.

History shows that when he speaks, prime ministers listen.

Dr Yunupingu has met with every Australian leader since Billy McMahon who served as the 20th prime minister from 1971 to 1972.

When he has felt disrespected, such as by Tony Abbott in 2014, the politicians quickly make amends.

Mr Wyatt was in the unenviable position of having to defend Mr Morrison's opposition to a voice to parliament, which the minister had supported.

But he warned every constitutional referendum that had failed had sent the issue into permanent retirement in Australia, and he had to get it right for "our children and those who come in the future".

"It is too critical to fail ... if that happens the indelible imprint it will leave on the psyche of indigenous Australians, plus all those who support us," he told reporters at Garma.

"So we have to be very considered, very measured, but we have to consider all the other options."

The Uluru Statement that kickstarted the push for a "First Nations Voice" also called for a Makarrata Commission on agreement-making and truth-telling.

Mr Wyatt opposes a South African-style reconciliation commission, but wants Australians taught "the truth" about indigenous history, such as the massacre of Aboriginal people after colonisation.

Universities and schools must accept they are part of "the process of truth-telling of this nation", he said.

Those who oppose the Uluru Statement say the priority should be "closing the gap" and improving Aboriginal lives; it is divisive to give a specific race a place in the constitution; and would create a third chamber that undermines Westminster parliamentary democracy.

Closing the Gap has been the policy to tackle Aboriginal disadvantage since 2008, but senior indigenous bureaucrat Pat Turner said at Garma there was an "almost obsessive government focus on targets" that were never met, creating a tale of woe.

The latest move is a coalition of 40 non-government Aboriginal peak organisations joining the nation's governments in running Closing the Gap in the hope it will help.

The Northern Territory government was accused at Garma of siphoning hundreds of millions of GST dollars a year, meant to address remote disadvantage, to pay for a massive public service and urban projects.

Accountant and former NT council of social services president Barry Hansen presented more than a decade's data that found the NT government at times underspent by $500 million a year funds that were supposed to be spent on indigenous disadvantage.

"If the Northern Territory government was a corporation, serious thought would have to be given to winding it up; if it was an Aboriginal corporation, its cabinet ministers would be prosecuted," said Denise Bowden, chief executive of the Yothu Yindi Foundation that runs Garma.

Former deputy PM Barnaby Joyce warned in 2017 that a constitutionally enshrined indigenous voice to parliament would be a "third chamber" but recently apologised and retracted the comment.

However, MPs such as Peter Dutton and the conservative Institute of Public Affairs continue to label the voice an undemocratic third chamber.

Cape York leader Noel Pearson attacked conservative columnists and the IPA over what he called their "campaign of lies and destruction of truth".

Western Australian Yawuru man and Labor senator Pat Dodson said he hoped Australia would evolve politically as New Zealand had with more First Nations people forming their own party or standing in mainstream parties.

But until then, Australia had to have a treaty process and "deal with the original injustice and substantive matters in contention between the settlers and those of us who have been colonised by settlers", he said.

"It will not undermine parliament, I think it will lead to a greater sense of unity for the nation," he told AAP.

Australian Associated Press