Prime Minister Anthony Albanese remains optimistic Australians will see through the Liberal Party's "disingenuous" opposition to an Indigenous voice.
Opposition Leader Peter Dutton confirmed the Liberals would back constitutional recognition for Indigenous people, but would not support a voice to parliament and executive government.
But the prime minister said Mr Dutton had been part of a government that was in power for nearly a decade but had not advanced the issues they now called for.
"We've waited 122 years to recognise in our constitution the privilege that we have of sharing this continent with the oldest continuous culture on Earth (and) I say to Australians: do not miss this opportunity," he told reporters in Sydney.
"We need to acknowledge that with the best of intentions and goodwill, what we have done until now is not working.
"We need to consult on matters that affect Aboriginal and Torres Strait Islander people."
Indigenous academic and one of the Uluru Statement's architects Noel Pearson said it was a sad day for Australia that there would not be bipartisan support for such an important national enterprise.
He said the Liberal Party had committed a "Judas betrayal" of the Australian people with its stance on the Indigenous voice.
"Nevertheless, I am certain that every attempt to try and kill and bury Uluru will not succeed (and) the Australian people will rise to the historic opportunity we have to achieve reconciliation at last," he told ABC Radio National.
Mr Pearson said the Liberal Party had made a "disgraceful attempt" to derail the Indigenous voice but he remained confident the referendum would succeed.
"I couldn't sleep last night. I was troubled by dreams and the spectre of the darkness of the Liberal Party's Judas betrayal of our country," he said.
"I've got a great belief that the Liberal Party is greatly out of step with the sentiment of the Australian people on this issue."
Mr Dutton said he had approached the proposal with an open mind and disputed claims by the prime minister that he had been consulted on the terms of the voice.
"The prime minister misrepresents those meetings ... I wouldn't frame it as a genuine engagement," he told ABC Radio.
Asked if his position could ultimately put him on the wrong side of history, Mr Dutton said he was in favour of practical outcomes for Indigenous people.
"The voice has turned into ... an opportunity for there to be input into every aspect of government work," he said.
"I don't believe that that is going to deliver the practical outcomes to Indigenous Australians that we all crave."
But Mr Albanese said the opposition leader's repeated referral to a "Canberra voice" demonstrated the disingenuous nature of the Liberal Party's position.
"Peter Dutton was part of a government for almost a decade that could have ... responded, legislated for issues that they're now talking about," he said.
"This is a divisive position that Peter Dutton has taken, this is opportunistic.
"(The coalition) have opposed just about every piece of legislation that's been before the parliament and now they're shrinking further into negativity with their opposition."
The model put forward by Labor would add a new section to the constitution recognising Indigenous people and enshrine a voice.
The Uluru statement included a call for the establishment of an Indigenous voice, which it said should be enshrined in the constitution.
