Aboriginal and Torres Strait Islander leaders have rejected the idea of constitutional recognition and will instead push for a constitutionally enshrined Indigenous voice in parliament and a commission that will lead to a treaty.

After a meeting of more than 250 community leaders at Uluru, referendum council member Professor Megan Davis delivered a powerful statement from the group asserting that sovereignty had never been ceded or extinguished.

The statement said that the high rates of incarceration, youth detention and child removal showed the need for a significant practical change, not a symbolic reform.

“These dimensions of our crisis tell plainly the structural nature of our problem,” it said. “This is the torment of our powerlessness.

“We seek constitutional reforms to empower our people and take a rightful place in our own country. When we have power over our destiny our children will flourish. They will walk in two worlds and their culture will be a gift to their country.”

It said a makarrata, a Yolgnu word for treaty, was “the culmination of our agenda”.

“In 1967 we were counted,” the statement read. “In 2017 we seek to be heard.”

The outline for reform followed a statement that Aboriginal and Torres Strait Islander peoples were the sovereign first peoples of Australia.

“This sovereignty is a spiritual notion ... It has never been ceded or extinguished, and co-exists with the sovereignty of the crown,” the statement read. “With substantive constitutional change and structural reform, we believe this ancient sovereignty can shine through as a fuller expression of Australia’s nationhood.”

The statement was the culmination of three days of meetings at Uluru, which followed six months of regional dialogues conducted by the referendum council.

It is a significant departure from the more symbolic forms of constitutional recognition discussed by largely non-Indigenous politicians in the past, to which Malcolm Turnbull and Bill Shorten had given their support. But it is consistent with longstanding political campaigns by Aboriginal and Torres Strait Islander peoples, which have focused around securing a treaty.

The proposed treaty commission would be given the dual task of working towards a treaty and engaging in a public truth-telling process.

“Part of this healing of the nation and coming together and having a mature nation, there has to be proper truth-telling in the same way they have done in other countries in the world,” Davis said.

The meetings at Uluru went late into the night, with a number of delegates, including members of the referendum council, working until 4am on Friday to finalise what has been called the statement from the heart of the nation.

Five hours later the remaining delegates gave it their unanimous approval, responding with thunderous applause, cheers, whistles and a standing ovation.

Not all the delegates were in the room; seven walked out in protest at the process and the way the discussion was heading on Thursday, and not all returned.

Delegates were united in rejecting the proposal put forward with bipartisan political support in 2010 for a statement recognising and acknowledging Aboriginal and Torres Strait Islander peoples as the first peoples of Australia to be inserted into the constitution.

“All of the dialogues, including the one-day information session in Canberra, rejected totally outright having some sort of acknowledgment in the constitution,” Davis said. “That was totally rejected by all of the meetings and everybody we’ve spoken to over this six-month period.”

The statement also rejected the word recognition, instead calling the proposed changes a reform.

That leaves the federally funded Recognise organisation, which has received millions of dollars in funding over the past five years to gather support for the “recognise” movement, in a difficult position.

But that is not a concern for the delegates or the referendum council, who have been focused on outlining their key demands from any potential reform.

The central plank is the proposed parliamentary voice for Indigenous peoples, a suggestion championed by Cape York leader Noel Pearson.

In an article in the Australian Law Journal this month, Pearson and Cape York Institute constitutional reform research fellow Shireen Morris argued that inserting a new section of the constitution establishing an Indigenous voice in parliament was “the only proposal for substantive and practical constitutional recognition which is both legally sound as well as potentially politically viable”.

In contrast, they argued, a constitutional protection against racial discrimination, which had been one of the most popular proposals going into the Uluru convention, could not be described as politically viable.

Les Malezer, a Butchulla and Gubbi Gubbi man and Australian delegate to the UN permanent forum on Indigenous issues, said Indigenous people did need a genuine voice in parliament to be able to direct and inform policy designed specifically to apply to Indigenous peoples, but said enshrining it in the constitution would not necessarily protect it from political interference.

“The government of the day can interpret what those words mean in the constitution,” he told Guardian Australia.

“So if it just says something like ‘There shall be a body representing Aboriginal people’, well it could be like Atsic [the Aboriginal and Torres Strait Islander Commission, unilaterally abolished by the Howard government in 2005] with 400 elected representatives … or it could be like the Indigenous advisory council led by Warren Mundine.

“A ‘body representing Aboriginal people’ is open to all forms of political design.”

Malezer said there was no proof such an amendment would succeed at a referendum. Both sides of politics have been at best lukewarm on the idea.

“We have really no evidence from polling the public to see that a proposal like that will have majority support,” he said.

The proposal has also been criticised by some Aboriginal and Torres Strait Islander people, who say putting a body representing them into the constitution itself abrogates their sovereignty.

That concern was the driving reason behind the walk-out of seven delegates and 40 observers on Thursday.

As a Victorian delegate, Lydia Thorpe, said: “We need to protect and preserve our sovereignty. We demand a sovereign treaty with an independent sovereign treaty commission and appropriate funds allocated.”

The strong words asserting sovereignty in the Uluru statement are unlikely to appease those concerns.

Two delegates from each of the 12 dialogues, and a range of other interest groups and experts, have formed a working group to pursue the changes with parliament and continue consultation with the community.

“It’s this generation’s turn to have a run at it, and we’re going to run at it head-first and butt it down and make it happen this time,” Davis said. “Our very survival in fact depends on it.”