Labor leader Anthony Albanese would work quickly to establish a Voice to Parliament for Australia's Indigenous people should he become prime minister after the federal election.
He says it is not about a third chamber for parliament but establishing politeness and good manners so that if there is an issue that affects the health, education, housing and lives of First Nations people they should be consulted.
"This is a change that has been a long time coming. We've been talking about it since at least the end of last century," Mr Albanese told the ABC's Insiders program on Sunday.
"I will consult with First Nations people about the timetable. I will reach out across the parliament ... to try to secure support as much as possible."
He said it should be recognised in the constitution that Australia's history did not begin in 1788.
"This is a nation changing moment. Just as the apology to the stolen generations made our country stronger, this is a generous offer for First Nations people," he said.
Mr Albanese said Prime Minister Scott Morrison had promised to act on this during the last term of parliament.
"He doesn't want a Voice to Parliament. The only voice Scott Morrison ever wants to hear is his own," he said.
But deputy Liberal leader and treasurer Josh Frydenberg says constitutional recognition is important.
"That's been a consistent position of not just this prime minister but a previous prime minister," he told the Insiders program.
He said what the government has been focusing on are "regional voices".
"That's what (Indigenous Minister) Ken Wyatt has done a lot of work (on) and received support from the local Indigenous community to do so," he said.
"We have put significant funding in the budgets in order to focus on those regional voices."
Asked directly if he supported a Voice to Parliament in the constitution, Mr Frydenberg said: "I think this debate has some way to go."
"I do see some challenges with it and ultimately Australia would be best served by having a bipartisan approach on this, but we do support constitutional recognition of our first Australians."
Australian Associated Press