Indigenous Australians have rejected a referendum that offers only minimal recognition in the constitution, insisting they will walk away unless more meaningful change is offered.

They have challenged political leaders to discuss what is emerging as their key proposal, an Indigenous body being recognised in the constitution, or be prepared to leave the recognition challenge to the next generation.

After seven of 12 planned Indigenous-only dialogues, it is clear that a statement recognising Aboriginal and Torres Strait Islanders in the nation's founding document and some "tinkering" with the race power will not win Indigenous support.

"Aboriginal people will not accept a feel-good, symbolic stamp on a fundamentally unfair system," say Jeremy Clark and Jill Gallagher, the co-convenors of the latest dialogue, held in Melbourne over three days.

"The system needs to be improved. We need to change the way we do business in Aboriginal affairs. Constitutional recognition must mean real reform. It must create a genuine paradigm shift, or Aboriginal people will reject it," they said.

"People are being clear-eyed. They don't want to forgo history by taking whatever is on offer," Pat Anderson, the co-chair of the Referendum Council told Fairfax Media. "What is emerging from all the dialogues so far is a line in the sand: we are not accepting minimalism.

"[People] clearly understand they are part of a struggle that goes back to the 19th century - and we owe it to past leaders like Sir Doug Nicholls, William Cooper and so many others, to not accept reform that is no improvement on 1967 and just a bit of editing. There has to be substantial change," Ms Anderson said.

A 1967 referendum ended the practice of not counting Aboriginals and Torres Strait Islanders in the population and gave the Commonwealth the power to make laws for Indigenous people.

Ms Anderson conceded that Indigenous leaders faced a "hard sell" to win the support of Prime Minister Malcolm Turnbull and other politicians, but added: "Our brief under our terms of reference was to go out and ask Aboriginal and Torres Strait Islander people what they want - and this is what's emerging."

The nation's most senior Aboriginal politician, Aged Care and Indigenous Health Minister Ken Wyatt, recently urged those attending the dialogues to think big but be prepared to accept a judgment by political leaders on what is likely to secure passage of the referendum.

The emphatic view to emerge from the dialogues is that Aboriginal people will oppose anything they consider inadequate and could even mount their own "no" case to minimalist recognition.

Ms Anderson said an Indigenous body recognised in the constitution was emerging as the preferred vehicle to deliver substantial reforms. The Referendum Council has commissioned work on what such a body would look like and this would be produced in coming weeks, she said.

"At the moment it's just a framework, but people are definitely sold on the idea that we must have some input, locked into the constitution, where we can talk directly to Parliament as equal partners."

There are five more Indigenous dialogues before an Indigenous constitutional convention at Uluru on the weekend leading up to the 50th anniversary of the 1967 referendum in May.

Mr Clark and Ms Gallagher said the Melbourne dialogue saw healthy debate about sovereignty and treaties, "but one basic fact was clear: our people want real change, not minimalism".

The concern of many delegates at the dialogues is that politicians have already agreed on a "minimalist model" they consider capable of winning support at a referendum. This would involve removing section 25 of the constitution, which says the states can ban people from voting based on their race; minor change to the race power and the addition of some symbolic words of recognition.

The co-convenors of the Melbourne dialogue said a voice to Parliament, in the form of an Aboriginal body embedded in the constitution, emerged as a strong priority in the discussions.

"This body could consult on laws and policies about our people, to help hold government to account. It could work under and incorporate the principles of the UN Declaration on the Rights of Indigenous Peoples, which could be articulated in statement of acknowledgement or a legislated declaration," they said.

"The body could help drive reforms to enable agreement-making, so that a truth and reconciliation process can be pursued. As delegates pointed out: we can't have reconciliation without having some truth."

Mr Wyatt, the first Indigenous person to be elected to the House of Representatives and the first to be appointed to the executive of the Commonwealth government, recently said he was opposed to having an Indigenous body enshrined in the constitution, and did not believe it would be supported by the broader population.

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