Malcolm Turnbull has been accused of "egregious dog whistling" after his government walked away from a proposal for a constitutionally-enshrined indigenous voice in parliament.
During a summit at Uluru in May, indigenous leaders rejected symbolic constitutional recognition in favour of an elected parliamentary advisory body and a treaty.
But Mr Turnbull insists a new representative body was not desirable or capable of winning acceptance at a referendum.
On Thursday, he said the government had listened carefully to the arguments put for a new body and recognised the desire for indigenous Australians to have a greater say in their own affairs.
But warned it would inevitably become seen as a third chamber of Parliament.
Cape York leader Noel Pearson said at least former prime minister John Howard had the grace to put the public question of a republic to the Australian people for their vote in 1999.
"There could have been a way to say no to this, without all the egregious dog whistling that is present in the prime minister's press release," Mr Pearson told ABC radio.
Opposition Leader Bill Shorten and indigenous Senator Pat Dodson said Mr Turnbull had thrown away years of hard work and goodwill by ignoring the legitimate aspirations of the Aboriginal community.
"There's nothing honourable about what's happened here," Senator Dodson told ABC radio.
"It wasn't honourable because they didn't discuss any of this with their own advisory committee (or) the indigenous leadership."
Senator Dodson said who knows whether the body would pass the referendum test.
"We've just spent $122 million surveying people on the question of same sex marriage ... we could have taken the same approach here."
Greens Senator Rachel Siewert said cabinet's decision makes a "mockery" of the government's claim that they listen to indigenous people.
Josephine Crawshaw, who is involved in the Uluru statement group, said there was a sense of "groundhog day" for indigenous people.
"After a decade of discussions and millions of dollars spent on constitutional recognition it is unfortunate we have come to this," she said.
"We have come to a point where seemingly no action will be taken."
The National Congress of Australia's First Peoples said the decision was sending "shockwaves" through indigenous communities.Suggest a correction