Incoming Labor minister Linda Burney has urged Peter Dutton to end a decade of "divisive" politics and back a First Nations Voice to Parliament, saying there is "no shame" in growing on Indigenous recognition.
Ms Burney will be sworn in as Minister for Indigenous Affairs on Wednesday - the first Indigenous woman to hold the post - and declared "I will not fail" in implementing the Uluru Statement from the Heart.
Delivering a Reconciliation Week address to the Don Dunstan Foundation on Tuesday, she framed the issue as an opportunity for Mr Dutton, who walked out on the Apology to the Stolen Generations in 2008, to show his "much-talked-about different side".
But Ms Burney stressed there was "no shame" in growing on Indigenous recognition, which was central to "the journey of reconciliation".
"There is no one for whom supporting a referendum for a Voice to Parliament represents a bigger political opportunity than for Peter Dutton," she said.
"After a decade of divisive political discourse - of lifters and leaners, of those who have a go and, by inference, those who don't - this is an opportunity for unity and for leadership.
"It's also about being on the right side of history ... it is a path I would be very pleased to walk with Peter Dutton and the Liberal Party."
Mr Dutton on Tuesday admitted he had made a mistake in boycotting the 2008 Apology, but was non-committal on backing the Uluru Statement, saying Labor had yet to finalise its plans.
Ms Burney urged her Liberal predecessor Ken Wyatt - who she described as a "pragmatic, thoughtful" friend - to sway his former colleagues, despite losing his seat at the May poll.
"In recent days I am very pleased that Ken has said he would support a constitutionally enshrined Voice ... And on this front, I say to Ken: I need your support, brother," she said.
Ms Burney said Labor aimed to complement the Uluru Statement with a range of practical measures to improve Indigenous lives, including justice reinvestment, boosted housing and services in the Northern Territory, scrapping the Community Development program, and working with business to lift First Nations employment.
She said the Voice to Parliament should not be "subject to the whims of the government of the day", placing it in the same lineage as the 1967 referendum which officially recognised First Nations people as Australians.
"Can you imagine, or remember, how it felt to walk down the street that week, looking your fellow citizens in the eye [and] knowing that together you had expressed your values and made your country a fairer place?" she said.
"Now imagine how this next referendum will make us feel about ourselves, our neighbours, and our country, when it passes. Walk with me in that future for a moment."
Ms Burney described then prime minister Malcolm Turnbull rejecting the Voice out of hand in 2017 as "profoundly disappointing", suggesting it was influenced by his support for the doomed republic referendum a decade earlier.
"[But] it was at least a better reason than Scott Morrison's retort during the recent campaign - 'Why would I?'" she said.
She said the major progress in bringing First Nations voices to the fore - Gough Whitlam returning Gurindji land soil to Vincent Lingiari, Paul Keating's Redfern address, and Kevin Rudd's Apology - had been delivered by Labor governments.
"Anthony Albanese and I want to add the next to this list ... I know Australia is ready for this," she said.