Delegates and experts involved in the Uluru dialogues have criticised Barnaby Joyce for misinterpreting a proposal to create a constitutionally enshrined Indigenous voice to parliament, and asked politicians not to dismiss the idea as “unwinnable” before reading the full report.

Amending the constitution to create a new Indigenous body that talks directly to parliament was one of the key outcomes of a three-day meeting of more than 250 Aboriginal and Torres Strait Islander people at Uluru last week and was the central platform of the Uluru statement, which received unanimous approval and a standing ovation.

Joyce said the proposal would not win the double majority required to pass a referendum.

“Look, if you’re asking for a new chamber in the federal parliament and some of the articles I see are sort of heading in that direction, that’s not going to happen,” he told Radio National on Monday. “I’m just going to be fair dinkum with people: we’ve got enough problems with the Senate we’ve got. We don’t need another one.”

Joyce said he supported constitutional recognition but it was “self-defeating” to propose something that the majority of Australians would not support.

“We’ve got to make sure that it’s saleable,” he said. “If you’re suggesting that we have local government, state government in the upper and lower house, then a federal government with a lower house, a Senate, and another chamber again … you don’t have to be Nostradamus to tell the future of what happens here. The Australian people will say no to that.”

The Uluru meetings were closed to politicians and the Referendum Council is yet to release its full report containing the detail of the proposals put forward in the working groups, which will be handed to the prime minister, Malcolm Turnbull, and the opposition leader, Bill Shorten, in June.

But those that were in the room said adding an additional Indigenous chamber of parliament, as Joyce presumes, was not on the table.

The constitutional lawyer Gabrielle Appleby attended 11 of the 12 regional dialogues held by the Referendum Council, and was also at the Uluru convention to provide legal advice and help drafting the proposals.

“That idea [of a new chamber of parliament] is not what was being discussed at the dialogues in the lead-up to Uluru and that wasn’t what was being discussed in the working groups,” Appleby said.

“We know that they want a voice in the political process. To say that they want to have a third chamber of parliament jumps the gun in terms of the detail of what we know about it.”

Most delegates who spoke to Guardian Australia about the proposed model at Uluru described it as a representative body that parliament would listen to when forming legislation that specifically affected Aboriginal and Torres Strait Islander peoples; something more closely resembling the dismantled Aboriginal and Torres Strait Islander Commission (Atsic) than another layer of government.

“What we did hear a lot was the understanding that Atsic was a statutory body and Atsic was able to be abolished by statute,” Appleby said. “They wanted to create something that was not vulnerable to being dismantled.”

Delegates at the Uluru meetings elected a working group to work with both politicians and the Indigenous community to finalise the reforms proposed in the Uluru statement.

“People in positions like [Joyce] should be careful not to be speculating that that’s what we want when it has not been finalised,” said Thomas Mayor, Northern Territory delegate and a Badhulgau and Kulkalaig man. “I think that he should invite the working group that has been elected to talk to him about that.”

The Referendum Council co-chair, Mark Leibler, asked people to withhold judgment on the proposal until they have seen the Referendum Council’s full report. He also described the voice to parliament as an “advisory body”.

Indigenous politicians Ken Wyatt, a Liberal MP, and Linda Burney, a Labor MP, said it was important that any option for reform was given bipartisan support.

Burney also raised questions about the proposals put forward in the Uluru statement, saying a constitutionally enshrined voice to parliament could have implications for the National Congress, and questioned why removing the race power was not listed as a priority out of the delegations.

Burney said it was important that any proposal be pragmatic.

“Whatever it’s going to be, looks like it won’t be successful, then you’d have to ask yourself, would you put the question to a referendum?” she told the ABC.

“We don’t want this process set back two or three generations. We want it to go forward and I think there is the will, the capacity and the determination to make that happen.”

The Uluru statement focused on a constitutionally enshrined voice to parliament and establishing a commission to investigate a makarrata or treaty because they were the key concerns throughout the dialogue process, the Referendum Council chairwoman, Pat Anderson, said on Friday.

The dialogues also comprehensively rejected a minimalist form of symbolic conditional recognition, like a constitutional preamble or statement of acknowledgement, in favour of those more substantive proposals.

Despite that statement, a number of politicians said they still supported a recognition statement.

“I do want to see Aboriginal people represented in the national constitution as they should always have been,” the Western Australian premier, Mark McGowan, said on Sunday.

“I think we should deal with that first before we move on to other issues.”

Shireen Morris, a constitutional reform advisor for Noel Pearson’s Cape York Institute, said the response from politicians to the Uluru statement showed why an Indigenous voice to parliament was needed.

This is exactly why Indigenous Peoples have asked for a constitutionally enshrined voice: their voice is sidelined in decisions about them. — Shireen Morris (@ShireenMorrisMs) May 28, 2017

“Indigenous people achieve united consensus on the kind of recognition they want, pollies and white experts immediately explain why they’re wrong,” Morris said on Twitter. “This is exactly why Indigenous peoples have asked for a constitutionally enshrined voice: their voice is sidelined in decisions about them

“As Australians, we need to back what Indigenous people are seeking here. It’s an achievable, smart consensus position. Let’s get behind it.”