Aboriginal leaders have vowed to continue to fight for a Constitutionally entrenched voice to Parliament despite the Turnbull Government's refusal to go to a referendum on the question.
Suzanne Thompson, the co-chair of a working group set up after the historic meeting of Aboriginal leaders at Uluru in May, said a series of strategy meetings had been held on how they would move forward.
"I think the majority of Australians want to see some change," she said.
"We're a patient people. We're very patient. How long have we been waiting for this?
"We're definitely not beaten by this. If anything, it's just raising the bar."
Her comments came as a national survey carried out by four top universities found widespread support for Indigenous Constitutional recognition, including a voice to Parliament.
The online survey reported 71 percent of respondents generally supported recognition â€" 34 percent strongly â€" and 61 percent supported a voice to Parliament.
The results, released this week, were part of the Australian Constitutional Values Survey conducted in August by a team from Griffith University in Queensland, the University of NSW, University of Sydney and the Australian National University.
The survey was conducted online by OmniPoll among a random sample of 1526 adults from all states and territories.
"The results were clear and surprisingly strong," said Dr Paul Kildea, senior lecturer in law at the University of New South Wales.
"Not only did general support for Indigenous Constitutional recognition remain strong â€" specific support for the idea of a representative Indigenous advisory body was much stronger than expected for such a relatively new proposal.
"Based on this evidence, the idea that an Indigenous advisory body is incapable of winning acceptance at a referendum is simply unfounded."
Support for general recognition in the Constitution was strongest in NSW, Victoria and Queensland and for a voice to Parliament in Victoria, NSW and Queensland.
Only in Tasmania did support for a voice to Parliament not have majority support.
First People's communities across Australia were shocked and disappointed last week when the Turnbull Cabinet rejected the Referendum Council's recommendations on a voice to Parliament.
Instead, a parliamentary committee may now be set up to look at other proposals including the Makarrata Commission.
The National Congress of Australia's First Peoples said this week if a joint select committee was set up, it must have a seat.
Congress co-chair Jackie Huggins said people were disappointed the Prime Minister and Cabinet had not heard the aspirations of Aboriginal and Torres Strait Islander people across Australia.
Her co-chair Rod Little said "no people need permission from government" to bring about change.
Reconciliation Australia said the Federal Government had missed the opportunity to take action on long-fought Constitutional recognition of Aboriginal and Torres Strait Islander peoples.
Reconciliation Australia chief executive officer Karen Mundine said the Prime Minister's decision was a blow to Aboriginal and Torres Strait Islander Australians who had participated in the government-initiated Referendum Council process in good faith.
"The Government asked Aboriginal and Torres Strait Islander peoples what they wanted, they delivered a consensus and then the Government rejected it out of hand, without adequate dialogue or evidence," she said.
Opposition Leader Bill Shorten and Labor Senator Pat Dodson said Mr Turnbull had thrown away years of hard work and goodwill by ignoring the aspirations of the Aboriginal community.
Greens Senator Rachel Siewert said the cabinet decision made a mockery of the Government's claim that it listens to Indigenous people.
The proposal for a voice to Parliament followed a year of national consultation with Indigenous communities that culminated with a summit of 300 leaders at Uluru in May and the Uluru Statement from the Heart.
The Uluru Statement Working Group was set up by leaders to follow the statement through with government.
Wendy Caccetta