A poll released by Essential found that 70 percent of 1,097 respondents supported constitutional recognition for Aboriginal and Torres Strait Islander people, with 18 percent opposed and 12 percent undecided.
Australia will hold a national vote within three years on whether to include recognition of indigenous people in its constitution, the government said on Wednesday.
Any referendum question must be supported by the majority of Australian voters, as well as at least four out of six states.
Indigenous leaders proposed in 2017 establishing an advisory body comprised of elected indigenous Australians enshrined in the constitution.
"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 (Aboriginal) indigenous affairs minister".
"I am prepared to walk with people on all sides of politics, all sides of our community to hear their views and reach a point in which they can agree", he said.
Labor leader Anthony Albanese on Thursday declared that a successful referendum on recognition was "realistic and doable".
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What it simply said was that there is a need for an indigenous voice to parliament, without any power to determine legislation. "It is as simple as that".
But if the proposal included an idea like the "First Nations voice" set out in the Uluru Statement from the Heart then that was unacceptable to him, and he predicted it would be unacceptable to like-minded Coalition colleagues.
Prime Minister Scott Morrison will reportedly veto any move to enshrine an indigenous voice in the constitution.
"We all know how hard it is to achieve referendum change in Australia on any subject", opposition shadow minister for indigenous Australians Linda Burney, who is also Aboriginal, told national broadcaster ABC.
"If the voice fails in any referendum, and if we were to put it up and it was not going to be accepted, then it is folly".
"Labor has been saying clearly that we would like a voice entrenched in the Australian constitution, and I know that there are many people on the government benches that also believe that", said Linda Burney, the shadow minister for Indigenous Australians.
But the deputy prime minister also appears to be kicking the can down the road.