On Friday, hundreds of Indigenous leaders at Uluru abandoned the prospect of a statement of acknowledgement in the constitution recognising Aboriginal people as the original owners of the land.
Instead, they decided to push for a constitutionally elected Indigenous body in federal parliament, a mechanism for treaty making and a healing commission.
"In 1967 we were counted, in 2017 we seek to be heard," Indigenous leaders at the Referendum Council summit in Uluru said on Friday.
Mr Turnbull told the National Reconciliation Week lunch in Melbourne to mark the 50th anniversary of the 1967 referendum and the 25th anniversary of the Mabo decision that Australians were "constitutionally conservative".
"This week has seen us look towards another step, with the Referendum Council's National Convention at Uluru," he said.
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He noted the "last remotely controversial amendment to be approved was in 1946".
"History would indicate that to succeed not only must there be overwhelming support but minimal, or at least tepid, opposition," he said.
He said political unity was needed to persuade the "constitutionally conservative nation" to vote in favour of change.
Opposition Leader Bill Shorten told the lunch there was "a sincere desire for bipartisanship" on the referendum issue.
Recognise, which is a part of Reconciliation Australia, will provide details of the new proposal in its final report to Mr Turnbull and Mr Shorten on June 30.
Mr Turnbull and Mr Shorten were tight-lipped on Friday, saying they did not want to pre-empt the final recommendations of the Reconciliation Council.
Greens leader Richard Di Natale has called on the prime minister to take heed of the Uluru outcome.
"Malcolm Turnbull, listen to the voice of Aboriginal people, establish a representative body and make sure that Aboriginal voices are heard throughout this nation."
The political leaders on Saturday will join the Long Walk to the MCG for the Indigenous round of the AFL.
