Ms Burney will use the 15th anniversary of the historic apology to send a message to those, including Mr Dutton, who walked out of parliament on then-prime minister Kevin Rudd's formal apology in 2008.
Mr Dutton said he regretted his decision to boycott the apology after he became Opposition Leader last year in May.
"I understand the symbolism and I made a mistake," he said.
In a speech at the Healing Foundation in Canberra on Sunday, Ms Burney will say it's easy to claim the apology "didn't fix everything," but was about "healing a deep wound" after successive government policies which failed Indigenous Australians.
"I know that some people who boycotted that historic day in 2008 have since expressed their regret," she will say.
"They now admit that it was a mistake. Don't make the same mistake again.
"When a generous and gracious hand is outstretched – in partnership – it should be grasped.
"To do anything else would be to repeat the mistakes of the past."
Ms Burney will say the apology was also the "catalyst for important practical change" including Closing the Gap targets.
She will say now is the time for embracing new ways to address challenges where "old approaches haven't worked".
A referendum on enshrining an Indigenous voice in the constitution will be held in the second half of the year, while legislation to enable the vote is expected to be introduced to parliament in March.
Deputy Liberal Leader Sussan Ley said the coalition supported constitutional recognition, but the government had made the mistake of tying it to the voice, an advisory body which it can't properly explain.
"Don't take the high moral ground on this Anthony Albanese, simply deliver the explanation about the genuine engagement that you think this voice and the detail of the voice will bring," she told Sky News.
"It's all about the outcomes that Australians want to see."
Mr Dutton is yet to announce his party's position on the voice, while the Nationals will oppose it.
Labor Minister Jason Clare said there is high support for the voice in blue-ribbon seats previously held by former treasurer Josh Frydenberg and former prime minister Malcolm Turnbull, which were lost to the teal independents last year.
"I really do hope that the coalition finds it in their heart to get to this position," he told Sky News.
"Even if they can't find it in their hearts, I hope they find it in their heads, because if they oppose this, they'll never win those teal seats back."
