A Newspoll, conducted for The Australian, shows support for constitutional change has fallen to 38 per cent, while backing for the 'no' vote has risen to 53 per cent.
An October 14 referendum will ask Australians if they wish to recognise Indigenous people in the constitution as well as enshrine a proposed advisory body called the voice.
Consecutive polls have shown support for the voice has been sliding.
Success will require a majority of voters and a majority of states voting in favour.
Cabinet minister Tony Burke said he was very confident the referendum would succeed.
"Peter Dutton, I think has underestimated the goodwill of a whole lot of Liberal voters here as well," he told ABC radio on Monday.
"There's a generosity in the Australian people and as people come closer to the date, focus their minds, look at the proposal, we see something where there's nothing to lose and everything to gain."
Opposition Leader Peter Dutton has confirmed he would hold a second referendum solely to enshrine Indigenous recognition into the constitution if the voice fails to pass.
The polling also shows support for the coalition has reached its highest level since the federal election last year, with the opposition now leading 37 per cent to Labor's 35 per cent on primary votes.
But Labor still holds a comfortable lead on a two-party preferred basis, 53-47 per cent.
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