But the voice would not be consulted on every piece of legislation before the federal parliament as some raised concerns about a two-tier system.
Ms Burney said the voice would address two key issues; not recognising Australia's First Nations people are the longest continuous culture on the planet and improving the lives of Indigenous people.
"There is not equity in this country. Whatever government's done in the past, has not filled those gaps," she told Sky News on Sunday.
"This is an opportunity at nation building."
The Indigenous affairs minister says it would only consult on issues that "affect directly the lives of First Nations people".
"Things like land rights, legislation, things like native title, things like cultural water allocations, things like childcare," she said.
"So why pick on things like taxation or defence and some of the other nonsense that's been sprouted in the last few weeks."
Ms Burney says she remains optimistic over the position of Opposition Leader Peter Dutton.
"What I'm really encouraged about is that Peter Dutton continues to say that he's got an open mind," she said.
"Some of the points that Mr Dutton raises are really, really important points."
But Mr Dutton on Friday accused the government of not having a consistent message on the proposed Indigenous body and referendum.
"I see (Senator) Pat Dodson is now talking about legislation, I don't know that Linda Burney is," he told reporters.
"They all seem to be on different timelines."
Ms Burney rebuffed the suggestion, saying legislation would also be needed to enable a referendum and the parliament would always be in charge of the body's shape.
"I'm not sure why Peter Dutton would say things like that. Of course, there's legislation required, the machinery bills or the Referendum Act" she said.
"At the end of the day, it'll be the parliament that will design what the voice looks like."
But while Mr Dutton said the opposition hadn't reached a position on whether it would support the voice, former minister and Nationals MP Keith Pitt told Sky News he wouldn't.
"We are one people, we are one country," he said on Sunday.
"I don't see how this helps one kid get educated or prevents one domestic violence attack or helps one individual get a job.
"I just think that it's not the priority."
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