The former co-chair of Prime Minister Malcolm Turnbull's Indigenous Advisory Council has urged Indigenous leaders to "stay at the table" and not "have tantrums" while working towards constitutional recognition.

Key points: Chris Sarra says Indigenous elders expect their leaders to "stay in the conversation"

Chris Sarra says Indigenous elders expect their leaders to "stay in the conversation" The Coalition rejected the Uluru Statement from the Heart last year

The Coalition rejected the Uluru Statement from the Heart last year The statement called for an Indigenous voice to Parliament and a Makarrata Commission

Chris Sarra told the ABC's National Wrap program Indigenous Australians' voices had grown stronger over the past few years.

"We're saying we've got no sense of voice, but here we sit in a very privileged and very serious position speaking directly to the Prime Minister and directly to all ministers — that's something that we take very seriously and is something that never happened 18 months ago," Professor Sarra said.

"We can't, as Aboriginal leadership, flop around and have tantrums and be victims because the Uluru Statement was rejected."

The Uluru Statement from the Heart called for a constitutionally enshrined "First Nations Voice" to Parliament, and the establishment of a Makarrata Commission "to supervise a process of agreement-making between governments and First Nations and truth-telling about our history."

The Coalition rejected the statement, claiming its recommended advisory body on Indigenous affairs would be "seen as a third chamber of Parliament" with veto powers.

Professor Sarra warned Indigenous elders would expect leaders to "stay in the conversation" regardless of that rejection, and remain committed to the statement's core.

He predicted the notion of enabling a sense of voice would continue to exist until the matter was "embraced adequately and seriously".

'Strength-based' Indigenous policy needed

Professor Sarra challenged each minister to "embrace the challenges" of dealing with Aboriginal and Torres Strait Islander constituents. ( ABC News: Jake Evans )

Professor Sarra has spent the past 18 months advising the Prime Minister on how to engage directly with Indigenous Australians, rather than "sub-contracting those profoundly important relationships out to those gravy train charlatans".

He said switching from a "deficit based approach to a strength based approach" was high on the agenda during discussions with the Government, over the two-day sitting of the Indigenous Advisory Council in late June.

"We should never underestimate the power of getting the Prime Minister to change his rhetoric and embrace the notion of doing things with people, not to people," he said."

Professor Sarra cited the tangible success created by initiatives such as the Indigenous Procurement Policy (IPP) as a step in the right direction.

The IPP was introduced in 2015 to drive demand for Indigenous goods and services and grow the Indigenous business sector, and he hailed the scheme for moving Indigenous policy towards self-sufficiency.

Professor Sarra recently resigned as co-chair of the Indigenous Advisory Council, telling the ABC he made the decision to avoid a conflict of interest with his new role as the director-general of Queensland's Department of Aboriginal and Torres Strait Islander Partnerships.

His parting challenge to the Government was for every minister "to embrace the challenges of dealing with Aboriginal constituents and Torres Strait Islander constituents", rather than passing the buck to the Indigenous affairs minister.

Watch Chris Sarra's full interview with National Wrap on the ABC News Channel at 9:00pm AEST tonight.