The Prime Minister made the concession in a meeting with the four leaders who proposed separate Indigenous conferences as the best means of securing Indigenous support for a recognition model.

"It is the rumble we had to have to get the ground rules right, to get the understanding clear, but now we're very positive that we've got this show back on the rails," Cape York leader Noel Pearson declared after the meeting.

"This is a win for all Australians to know that the people that this referendum is about will have a genuine say in what goes forward," added Kirstie Parker, the co-chair of the National Congress of Australia's first Peoples.

Patrick Dodson also hailed the meeting as a positive step, but called on eminent Australians in all areas to show more leadership on the issue. "I'd like to see other leaders standing up and encouraging the politicians to be less timid," he said.

Mr Abbott has now agreed to an approach to achieve Indigenous consensus that is "broadly in line" with the proposal crafted by Mr Pearson, Professor Dodson, Dr Megan Davis and Ms Parker last month.

As reported exclusively in Fairfax Media, the shift follows a meeting between Mr Abbott and Mr Pearson last week in Brisbane, where the Indigenous leader argued the proposal represented the process most likely to produce a successful referendum.

The agreement should set a positive tone for Mr Abbott's week-long visit to Indigenous communities in the Torres Strait and at the tip of Cape York in far-north Queensland next week.

Although he denied an "about-face", Mr Abbott had formally rejected the proposal in a letter to the four on July 28, saying it risked producing "something akin to a log of claims that is unlikely to receive general support".

His concession came during a meeting at Parliament House lasting about 30 minutes before lunch on Thursday. The four separately met with Opposition Leader Bill Shorten, who had already backed Indigenous-only conferences.

While the Indigenous leaders' preference was for the Indigenous conferences to precede mainstream conferences, they have agreed that the two processes will run concurrently. "We are confident that the views that are expressed out of our process will inform what goes forward," Ms Parker said after the meeting.

In a concession to Mr Abbott, they have also agreed that the conferences will be run by a referendum council responsible for all consultations, rather than by a partnership of Indigenous organisations.

The referendum council will be announced soon by the Prime Minister and Mr Shorten. It will comprise equal Indigenous and non-Indigenous representation.

Speaking to reporters before the meeting, Mr Abbott said: "What I want to do is to ensure that we have a unifying and unified process which will produce, I hope, a national consensus towards the middle of next year that can then go to the people in the next term of Parliament.

"What we want to do is to have a unified process which certainly will involve Indigenous people talking, it will involve the wider community talking. And what I want to see is not some kind of them-and-us process but a we-the-people process."

But he said that within a "we-the-people process", it was important "for Indigenous people to have a chance to talk this through as thoroughly as possible".

In his letter of July 28, Mr Abbott insisted an Indigenous position should form "at the same time that a general community position is also forming", and maintained the proposal for a separate Indigenous conferences "jars with the notion of finally substituting 'we' for 'them and us"'.

Indigenous leaders felt so strongly about the need for Indigenous conferences that they were willing to proceed independently if the government chose not to fund an "Indigenous-specific process".

Mr Dodson co-chaired the expert panel that reported in January 2012 and supported the insertion of a new clause in the constitution banning racial discrimination by government.

Mr Pearson initially proposed the ban but has put forward an alternative model because he believes the ban will be opposed by constitutional conservatives and could have unintended consequences.

His model would lead to a new Indigenous body being recognised by the constitution with a voice to the national Parliament.

Both leaders have agreed to throw their unqualified support behind whatever model emerges from Indigenous conferences.

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