Sixty per cent of Australians support a proposed model of Indigenous recognition the federal government has dismissed as having no realistic chance of getting past a referendum, according to polling released on Monday.

The online survey, conducted by OmniPoll in August for researchers at Griffith University and the University of New South Wales, found that 60.7% of respondents broadly supported a proposal to “change the constitution to set up a representative Indigenous body to advise the parliament on laws and policies affecting Indigenous people”.

Of the 1,526 respondents, 24.1% strongly supported the proposal and 36.6% said they tended to support the proposal, while 16.9% said they tended to oppose it and 13.5% were strongly opposed.

The proposal received majority support in every state but Tasmania, where 49.1% of people opposed the idea. It also received majority support from Greens, Labor and Coalition voters, 80.3%, 67%, and 55.1% respectively.

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Dr Paul Kildea, from the University of NSW law school, said the results showed the government was “premature” in its rejection of the idea, which was formally put forward by the Referendum Council after the Uluru statement in May.

Malcolm Turnbull dismissed the proposal in a joint statement with the attorney general, George Brandis, and the Indigenous affairs minister, Nigel Scullion, on Thursday, saying: “The government does not believe such a radical change to our constitution’s representative institutions has any realistic prospect of being supported by a majority of Australians in a majority of states.”

Scullion said in Senate estimates on Friday that the government did not have any evidence to back up that view but that it was the government’s judgment that “if this notion of a voice was put to a referendum, it would certainly fail”.

The government’s response to the proposal, which was supported by 12 national dialogues and a gathering of 300 Aboriginal and Torres Strait Islander community representatives at Uluru, has been met with anger and frustration from many Indigenous people.

“It’s the ultimate symbol around the disrespect for Aboriginal people that the government in Australia has,” Nolan Hunter, who led the Broome delegation at the national convention in Uluru, said.

“It doesn’t tell me that the prime minister has taken Indigenous voices seriously. What we are really worried about is they are going to move something symbolic which the Australian people won’t support, and we know from the dialogues that Aboriginal people won’t support something symbolic.”

Kildea said the national support level of 60.7% shown in the polling was a “solid base” to build support for the proposal.

“I think what the polling shows is that the idea that the voice in parliament would not fly in a referendum is unfounded,” he said, adding that dismissing the proposal as an option without first fleshing out the details was “premature”.

“It’s concerning that the government would not take into account public opinion in making a decision of this nature... particularly given the energy and work that went into the Uluru statement.”

Kildea said it was too early in the process for the poll results to be considered a strong indicator of the outcome of a potential referendum.

“I think a better interpretation is that at this point in time the government has underestimated the public in terms of support for this proposal,” he said.

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The poll also asked respondents if they supported the general concept of recognising Aboriginal and Torres Strait Islander people in the constitution and whether they agreed that Australian governments should make formal agreements with Aboriginal and Torres Strait Islander people to recognise their rights.

The latter describes the treaty-making process that would be undertaken by a makarrata commission under the Uluru statement proposals.

The first question had broad support from 71.1% of respondents and strong support from 33.5%. Of the 21.3% who did not support the general concept of constitutional recognition, only 8.7% were strongly opposed.

It was supported in all states and territories, with the lowest level of support being Tasmania with 61.2%. It also had a high level of support among the three major political parties, with 68.5% support from Coalition voters, 76.3% support from Labor voters and 83% from Greens voters.

The question of agreement-making or treaties asked respondents if they agreed or disagreed that “there should be formal agreements between Australia’s governments and Australia’s Indigenous peoples to recognise their rights”.

It had the lowest level of support, with 58.4% of people nationally and a similar level of support in all states and territories except Tasmania, where 40.1% of people agreed and 48.2% of people disagreed. A majority of Greens, Labor, and Coalition voters agreed, at 73.6%, 64% and 54.7% respectively.

Griffith University professor John Parkinson, who worked on the polling, said he expected public support for the proposed Indigenous voice to parliament would be much lower. He said support for specific proposals was usually lower than support for the general idea of recognising Aboriginal and Torres Strait Islander people in the constitution.

Instead, he said, the response was “really strong.”

“Our evidence says that [the government’s] judgment might be off on this one,” he said. “Politicians have to use their political judgment. There are plenty of cases where that judgment has been better than the polling and there’s plenty of cases where it’s been the other way around.”

An earlier poll conducted by Essential in June, a week after the release of the Uluru statement, found that 44% of people supported the proposal of a constitutionally enshrined Indigenous voice to parliament and 41% were either undeclared or didn’t know.