The Newspoll conducted for The Australian newspaper and reported on Sunday night shows 46 per cent of all voters support the voice to parliament while 43 per cent are opposed and 11 per cent don't know.
The survey, of 1549 voters across the country between May 31 and June 3, was the first Newspoll to present respondents with the exact question that will be on the ballot paper when the referendum is held this year.
The question to be put to the Australian people in the referendum is: "A Proposed Law: to alter the constitution to recognise the First Peoples of Australia by establishing an Aboriginal and Torres Strait Islander voice. Do you approve this proposed alteration?"
A survey published in The Australian in April, which was an average of three Newspolls conducted between February and April, put support for constitutional change at 54 per cent with 38 per cent opposed and eight per cent saying they don't know.
The Newspoll published on Sunday showed women voters mostly in favour of the 'yes' side by 47 per cent compared to 40 per cent against.
Among male voters, 46 per cent were in the 'no' camp while 45 per cent backed the 'yes' side.
When divided along party lines, 63 per cent of Labor voters were in favour of the voice and 24 per cent were opposed while 28 per cent of coalition voters were in favour and 64 per cent against.
Former ACT chief minister Kate Carnell, who is heading up a Liberals for 'yes' campaign, said support will ramp up further once referendum legislation passes parliament later this month.
"We'll be able to move the campaign where it should be and that's down to grassroots Australia where it should be," she told ABC Radio on Monday.
"Really, this shouldn't be a political debate at all. It should be a debate out there in the community. It's every Australian that needs to vote on this."
The Liberals group is made up of Ms Carnell, along with former NSW premier Mike Baird, Tasmanian premier Jeremy Rockliff, ACT Opposition Leader Elizabeth Lee along with federal backbenchers Julian Leeser and Bridget Archer.
Ms Carnell said the constitutional changes proposed were safe options and would bring the country together.
"The message is, if we just do keep doing the same thing in this space, we'll end up with the same outcomes," she said.
"Liberals, I hope, will be focused on on getting practical change."
Prominent 'yes' campaigner Noel Pearson on Sunday accused Opposition Leader Peter Dutton of pushing a race-based argument he had promised he would avoid.
Mr Pearson said the coalition leader had previously assured him he did not take the voice to be a racial proposition.
He said he was therefore disappointed when Mr Dutton made a speech to parliament in which he said the voice would "re-racialise" Australia.
"The disappointing thing about the position taken by Peter Dutton is that I met with him two or three times with (former shadow attorney-general) Julian Leeser," the Indigenous campaigner told Sky News.
"At those meetings, Peter was very, very clear in what he said to me. He said, 'I do not agree with the race argument, don't take me to be making a race argument here'."
Mr Pearson said Mr Dutton was being "duplicitous" in now taking a different position.
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