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A clear majority of voters support recognising indigenous Australians in the constitution and creating a voice to parliament, according to a new poll.
Most also support a treaty with indigenous Australians, the Essential survey confirms.
Indigenous Australians Minister has committed to holding a referendum on constitutional recognition within the next three years.
But he and the prime minister are not going to support a constitutionally enshrined indigenous voice to parliament as proposed in the Uluru Statement from the Heart.
Liberal and National MPs have long raised concerns the indigenous advisory body could become a "third chamber" of parliament.
"We're not in favour of a third chamber or a separate voice," senior government minister Peter Dutton told the Nine Network today.
"We've got a very strong democracy, we want to see more indigenous people in the parliament, and it's great that Ken Wyatt is the first indigenous affairs minister.
"He's got a process that's underway, let him conduct the consultation and then we'll make an announcement about the next step."
As he tries to build consensus for the national vote, Mr Wyatt sought to calm his colleagues.
"It never was a third chamber," he told the The Sydney Morning Herald.
"It is about people, communities wanting to be heard."
The proposal for an indigenous voice to parliament - a key recommendation of the 2017 Uluru Statement - has been a vexed issue for the coalition government for years.
Prime Minister Scott Morrison and his predecessor Malcolm Turnbull have rejected enshrining a "third chamber" of parliament in the constitution.
Mr Morrison's constitutional view has not changed but he would consider a legislated national body comprising existing indigenous groups, The Australian reports.