Former prime minister Kevin Rudd has urged the Turnbull Government to reconsider its opposition to the Uluru Statement from the Heart.

A decade since he delivered a historic apology to the Stolen Generations, Mr Rudd said Australia needed another significant step towards addressing the legacy of dispossession.

"We're now up to a new set of challenges. It's never easy at the time. Had we not apologised 10 years ago, think for a moment what Australia would be like today," Mr Rudd said.

"To simply reject them coldly with a single statement, is simply wrong."

Prime Minister Malcolm Turnbull dashed hopes for a referendum to establish an independent Indigenous advisory body, deeming the idea too ambitious and unlikely to win support.

"The responsibility of political leadership is to explain that, rather than to demonise it," Mr Rudd said.

The Federal Government has said it remains committed to finding an alternative proposal to recognise Indigenous people in the constitution.

Indigenous leaders called for the "voice to Parliament" in the Uluru Statement from the Heart. ( ABC News: Stephanie Zillman )

"I would just appeal to Malcolm Turnbull to pause, and reflect and to consider the united voice of Indigenous people reflected in the Uluru Statement from the Heart," Mr Rudd said.

"I think it's far better to have a considered Indigenous voice made plain to the legislature, than a bunch of white folks saying, 'we think this is what Indigenous folks think'. I simply say, 'what's the big deal here'?"

The national apology was Mr Rudd's first act as prime minister in 2008 — he opened federal parliament with an emotive speech acknowledging generations of Aboriginal and Torres Strait Islander people forcibly removed from their families.

Saying sorry was a recommendation of the harrowing Bringing Them Home inquiry in 1997, which found that stolen children were "victims of gross violations of human rights".

Mr Turnbull will deliver an apology to survivors of child sexual abuse by the end of this year, and is urging states to join a national redress scheme.

Asked whether he regretted ruling out establishing a national Stolen Generations compensation scheme in 2008, Mr Rudd insisted he would have revisited the issue if he had remained as prime minister.

"What I was seeking to do at the time was bring the nation across along the apology divide. If you looked at the record of 2013, I said it was time for this to be considered afresh," he said.

"There's a lot of folk who have passed away, a lot who are very old, so, yes, it's time to move on that."

Rudd's reflections on saying sorry

His speech was hand-written, and only finished the morning of the apology.

"It's a small secret about the day itself which is I'd only finished writing the speech about 20 minutes before I walked in, because I wasn't happy about the way I'd concluded it," he said.

"After we'd greeted all the Aboriginal leaders at the ceremonial entrance, I had to go back to my office and finish writing. With a few minutes to go, I walked in with Albo [Anthony Albanese]."

Kevin Rudd (C) embraces members of Australia's Stolen Generation after delivering the apology in 2008. ( Mark Baker/Pool: Reuters )

Mr Rudd could not look up at the faces in the public gallery.

"When I stood up to begin delivering the apology, I did not trust myself to look into the eyes of our Indigenous leaders because I knew I would crack up and then break down," he said.

"I didn't want the day to be about 'prime minister breaks down in tears'; the day was about our Indigenous brothers and sisters.

"So, when people have asked me, 'why weren't you looking into the crowd?', there was a real reason for it — I know my own weaknesses and that's one of them."

He said the relief of the nation surprised him.

"What I found was just this overwhelming release of joy — undiverted joy. It was a day which was full of the spectrum of human emotions from a people who had being treated like animals," he said.

"What I thought was the remarkable response to the apology at the time — certainly one I didn't expect — was Australia in its guts feeling that we could do a lot better."