Malcolm Turnbull has been accused of lying by the Indigenous leader Noel Pearson over his rejection of a proposed Indigenous voice to parliament.

The prime minister had “lied” because he had previously suggested he supported the proposal back in 2015 and encouraged him on the issue, Pearson was quoted as saying.

The Uluru statement was drafted after a three-day summit of more than 300 Aboriginal and Torres Strait Islander community leaders and legal experts in May, which followed a year of consultation.

But the government rejected its recommendations, which include embedding an Indigenous voice to parliament in the constitution, saying a referendum proposing that change was “too ambitious” and would not get majority support.

On Sunday Turnbull doubled down on his opposition to the proposal, saying the work of the Indigenous advisory body was “not consistent with all of the work that had been done on the recognition agenda previously”.

He said the proposal was “contrary to the principles of equality and citizenship in Australia” and would be seen as a “third chamber” in the parliament.

Instead, the aim should be to increase Indigenous representation in the parliament.

“All Australians, whether they are a first Australian whose forebears have been here for 60,000 years, or whether they’ve just got their citizenship in a ceremony last week, have the same right to vote for, stand for and serve in our parliament,” Turnbull said.

But Pearson told the Australian: “He is lying; the fact is that he once encouraged me in relation to the voice.

“The drafting of the recommendations was done exclusively by [constitutional lawyer and University of New South Wales pro vice- chancellor] Megan Davis and Murray Gleeson, a former chief justice of the high court.

“If there’s insufficient detail or questions about whether it complied with the terms of reference and so on, that is down to the former chief justice of the high court – is he really saying that?”

More than 1,000 people, including the former Australian of the year Fiona Stanley, have signed a joint statement arguing the rejection of the Uluru statement “potentially compounds intergenerational traumas and their consequences” for Indigenous Australians and should be reversed.

Stanley, an epidemiologist who spent decades working in Indigenous communities, said the marginalisation of Indigenous Australians and their “virtual exclusion” from parliament and policy making was “a major reason for their current poor outcomes”.

“In spite of this, their resilience and strength is extraordinary and giving them the power to influence and change is urgent,” she said. “National and international studies on colonised Indigenous peoples show clearly that when they are able to implement the solutions developed by them, the outcomes are far better.

“Our research has shown also that the impact of previous practices of marginalisation and removal are responsible for a large part of today’s trauma and First Nations circumstances.”

She cited polling data that found that a constitutionally enshrined advisory body was supported by 60% of the Australian population. That is despite the prime minister arguing the proposal would have “no prospect at all of being successful in a referendum”.

The Australian Council of Social Service chief executive, Cassandra Goldie, said the rejection of the statement was “a deeply disrespectful act”.

“There is broad agreement among the general Australian community for constitutional reform regarding the rightful place of first nations peoples in our country,” she said. “We celebrated the Uluru statement and are now stunned that the First Nations leadership has been treated in this way.”

She said Indigenous leaders were “understandably disillusioned and frustrated by what has occurred”.

“Although we cannot change our past, we can determine our country’s future,” she said.

Turnbull’s office has been contacted for comment.