Aboriginal leaders have accused the Prime Minister of being "deceitful" and duplicitous for privately encouraging them to consult the Australian public on enshrining an Indigenous voice in the constitution before publicly rejecting the proposal.

Key points: Prime Minister Malcolm Turnbull slammed for comments on Indigenous constitutional recognition

Prime Minister Malcolm Turnbull slammed for comments on Indigenous constitutional recognition Indigenous Dialogues were to commence in two weeks

Indigenous Dialogues were to commence in two weeks Mr Turnbull says he was expressing an opinion

At the centre of the feud is a November 2016 meeting Mr Turnbull had with the Referendum Council, which was also attended by Opposition Leader Bill Shorten.

Cape York Indigenous leader Noel Pearson and other Referendum Council members are furious about the Prime Minister's answer to a question from Mr Shorten in Question Time on Tuesday.

Mr Turnbull told Parliament he had warned the council that "a representative body available only to Indigenous Australians" was "inconsistent with a fundamental principle of our democracy".

"I also said, being frank and honest, that I thought the prospects of such an amendment to the constitution being successful were absolutely zero, absolutely zero," the Prime Minister said on Tuesday.

However, after seeking clarification that they could consult on all models, the Referendum Council believed the PM would genuinely consider all proposals including the voice to Parliament, because he explicitly allowed them to consult on the option in writing.

Last year, Mr Turnbull killed hopes for a referendum to establish an Indigenous advisory body in the constitution, arguing the idea was too ambitious and would not win support across the country.

Mr Pearson said the Prime Minister "belled his own cat" with his answer to Parliament, "exposing his duplicity in relation to his dealing with Indigenous constitutional recognition" by misrepresenting what he told the council at the meeting.

"The Prime Minister had pre-judged the whole dialogue process even before the consultations with Indigenous people and the wider Australian community had even commenced," Mr Pearson said.

"His opposition to the 'voice' is based on his own opinion and takes no consideration of the outcomes of a public consultation process.

"The Prime Minister shows every week how poor his policy and political judgment is — why should this opportunity for recognition be lost because of his ineptitude and lack of imagination?"

He said Mr Turnbull was urging the council to "undertake a disingenuous process of pretending to consult with the public" about an option that he had already ruled out.

"Mr Shorten had left the meeting by the time the Prime Minister blurted out this viewpoint," Mr Pearson said.

"In response, I said to the Prime Minister, 'We are about to commence a national consultation process through a nationwide process of Indigenous dialogues, and are you ruling out one of the five options that are set out in the discussion paper? Would that not be disingenuous to not tell the public that the Government has foreclosed on one of the options?'"

Mr Pearson said the Prime Minister realised his error in the meeting and "tried to say that he was just expressing an opinion".

The Indigenous Dialogues were about to commence in two weeks.

In order to clarify matters the Indigenous members of the Referendum Council wrote to Mr Turnbull and Mr Shorten to clarify what they could consult on.

Letter: all models should be explored

The ABC has obtained a letter co-signed by Mr Turnbull and Mr Shorten in response to this, and sent to Referendum Council co-chair Pat Anderson on December 7, 2016, which explicitly said all models should be explored.

"We reaffirm the message we provided to the full Referendum Council on 25 November 2016: that the regional dialogues should proceed as planned, without delay, and that all models should be equally tested with the community," the letter said.

"We appointed the council to consult the community on constitutional recognition and to provide advice on how to progress toward a successful referendum.

"We ask that you test the views of all Australians, including Indigenous peoples, and report to us by 30 June 2017 as agreed at our meeting of 25 November 2016."

Sorry, this video has expired Turnbull adviser reveals Indigenous advisory body 'very much' on table

Mr Pearson told the ABC it was "on this basis that the Referendum Council proceeded with the dialogues that produced the Uluru Statement that recommended the voice to Parliament."

"[Mr Turnbull] committed in writing with the Leader of the Opposition that all options were still on the table. This was obviously deceitful on his part," Mr Pearson said.

"He had signed a letter making commitments that he did not believe. His answer in Question Time yesterday proves that."

Co-chair of the council Pat Anderson said she was deeply disappointed by the comments the Prime Minister made about the proposal.

"It's very disappointing the level of this whole discussion," Ms Anderson said.

"There does need to be a national conversation on this but the Prime Minister, by rejecting the Uluru statement, has decided not to go down that path."

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

But Professor Chris Sarra, one of Mr Turnbull's most trusted and influential Indigenous advisers, said other ways of delivering on the Uluru statement were now being explored in talks with the Government.

Professor Sarra was appointed co-chairman of the Prime Minister's Indigenous Advisory Council last year and is an internationally renowned educator.

A spokesman for the Prime Minister said the Referendum Council was asked to consult on all options and present their advice.