Prime Minister Tony Abbott is facing further criticism after rejecting the idea of Indigenous-led talks on constitutional recognition.

Several Aboriginal leaders want an Indigenous consensus on reform, before wider community consultations take place.

Indigenous leaders Patrick Dodson, Noel Pearson, Kirstie Parker and Megan Davis created a proposal for a series of conventions to allow Indigenous people to have their say first.

But Mr Abbott said there was a "risk" an Indigenous-only process might produce something close to a "log of claims".

"My anxiety about a separate Indigenous process is that it jars with a notion of finally substituting 'we' for 'them and us'," Mr Abbott wrote to the group.

"I am in favour of building consensus, but strongly believe this should be a national consensus in favour of a particular form of recognition rather than simply an Indigenous one.

"The risk with an Indigenous-only — or even an Indigenous-first — process is that it might produce something akin to a log of claims that is unlikely to receive general support.

"I accept these community conferences need to take place in a way that give Indigenous people ample opportunity to have their say."

Ms Parker, the co-chair of the National Congress of Australia's First Peoples, said she was dismayed by Mr Abbott's comments.

"The Prime Minister's talked about a more general process that we don't think is satisfactory, will make it difficult if not impossible for our people to arrive at some sort of broad position in any direction," Ms Parker said.

"What [Indigenous-only consultation] hopefully will lead to is an Aboriginal and Torres Strait Islander broad position.

"We are not giving up on the request that we've made to Government on this."

Ms Parker disagreed the proposal might lead to something like a "log of claims".

Prime Minister Tony Abbott said there was a "risk" an Indigenous-only process might produce something close to a "log of claims". ( AAP Image: Ben Macmahon )

"It's unfortunate to see it couched in that way because it really is ensuring that the people this referendum is about have a say in the sort of matters that are taken up in it," she said.

Indigenous leaders at the Garma Festival in East Arnhem Land yesterday expressed disappointment Mr Abbott did not accept the plan.

The ABC last night sought comment from Indigenous Affairs Minister Nigel Scullion and the co-chair of the constitutional recognition parliamentary committee, Liberal MP Ken Wyatt.

Opposition Indigenous affairs spokesman Shayne Neumann tweeted: "How deeply disappointing the PM has not accepted the proposal of respected Indigenous leaders."

Opposition Leader Bill Shorten said the proposal needed to be considered.

"We need to remain flexible on how we achieve constitutional recognition," he said.

"Part of that is ensuring Indigenous Australians have their views genuinely heard.

"I encourage Mr Abbott to keep an open mind about this proposal."