Labor leader Anthony Albanese has urged Prime Minister Scott Morrison to heed calls from indigenous, legal and business groups to advance constitutional recognition.
The opposition has backed the Uluru Statement, which called for an indigenous voice to parliament to be enshrined in the nation's founding document.
But Mr Morrison has continued the coalition government's opposition to the voice, despite growing calls for an official way to give Aboriginal and Torres Strait Islander people input into legislation.
"We need to advance Aboriginal reconciliation. Until we have that, we won't truly be a whole nation," Mr Albanese told the ABC's Insiders on Sunday.
The issue has been a key talking point at the Garma Festival of Traditional Cultures in northeast Arnhem Land where Mr Albanese has been this weekend.
He said the voice to parliament would not act as a de-facto third chamber of parliament, a leading criticism used by opponents of the proposal.
"Let's be clear about what First Nations people are asking for. Their ask is modest. It is simply that Aboriginal and Torres Strait islander people should be consulted on matters that affect them," he said.
Mr Albanese said the details of a voice to parliament would be decided by legislation, rather than in the constitution.
"When that hand of friendship is outstretched, the prime minister and myself should join together and shake that hand and move our nation forward. We'll be all the stronger for it."
Former High Court chief justices Robert French and Murray Gleeson have called for the voice, along with indigenous groups, powerful parts of the business community and unions.
Mr Albanese believes constitutional recognition would be similar to the apology to the stolen generation.
"Controversial in the lead-up, but once it happens, people would wonder what the fuss was about, because it wouldn't change, essentially, our parliamentary processes," he said.
"We can't move on to other constitutional questions until we deal with this unfinished business."
