Around 250 representatives from around the country met in Uluru and a report on the summit's position is to be submitted to politicians by the end of June.
Less than a week after the landmark summit, the response has been mixed.
The meeting in central Australia recommended establishing a federal parliamentary body to advise politicians on policy regarding First Peoples.
Speaking on the ABC's Q&A program, co-chair of the Referendum Council and chair of the Lowitja Institute, Pat Anderson, says it's time Indigenous Australians are given a voice.
She says despite a 1967 referendum in which Australians overwhelmingly voted to count Aboriginal and Torres Strait Islanders in the census, and allow the federal government to make laws for them, little has changed.
"In '67 we asked to be counted. In 2017 we're asking to be heard. We are voiceless and powerless in our own lands. This is our country. We have been here for 60,000 years. There has to be substantive change, structural change that will make a difference. We've been asking for this - nothing is new - since prior (to) 1840 and nobody listens and hears us. I don't understand that. What is it that we're not saying that you can't understand? I'm hopeful that this is an opportunity. I think Australia is ready for it. I think we're mature enough and sophisticated enough to have this - what might be a difficult conversation, but for goodness sake let's have it and be done with it."
Discussions in Uluru had been sometimes fraught, with several delegates walking out over demands for a treaty.
Founder of the Cape York Partnership Noel Pearson said the agreed-upon strategy is first to achieve an Indigenous advisory organisation.
"There's two doors here. We've got to go through one, the constitutional door, and then we go through a treaty and agreement door. We were asked to consult on a voice to Parliament, head of power, et cetera, including agreement-making. And the strategic consensus around the 12 dialogues reached at Uluru last week is we got to go through the constitutional door first and create a voice that is then in a position to sit down with Parliament and do agreements. That's the logic - through one door first, and then we approach the other door."
The idea has met a varied reception, with some Nationals politicians rejecting it outright.
Nationals leader Barnaby Joyce has warned it might destabilise support for the Uluru statement, which the Prime Minister has echoed.
Malcolm Turnbull says unanimous approval would be needed to effect any change, including constitutional recognition.
"So a referendum demands politicians to lead and we will. But a successful campaign for constitutional recognition must ask Australians to acknowledge the humanity of their neighbour, their fellow Australians, and harness support for the proposal with as much resolute solidarity and unity as the campaigners of '67 did 50 years ago."
But journalist Stan Grant used the ABC panel discussion to challenge politicians not to discount Australians.
"I think our politicians sell us short as a nation all the time. I don't think that there's enough faith in the capacity of Australians to understand and decide for themselves. Australians decide what Australia is. We define Australia. The other thing you don't want to underestimate is the persistence and the patience of our people. Don't underestimate the goodwill of Australians and don't underestimate the patience and persistence of our people because they're not going away."
The Referendum Council will meet next week to consider the Uluru declaration before submitting their report to Mr Turnbull and Opposition Leader Bill Shorten before June 30.
