Legislation to create an Indigenous voice to government should pass Federal Parliament before the next election, according to Minister for Indigenous Australians Ken Wyatt.

The Coalition has faced criticism for ruling out enshrining such a voice in the constitution, despite it being called for in the 2017 Uluru Statement from the Heart.

Mr Wyatt argued changing the constitution was a fraught process, with only eight out of 44 referendums in Australia's history proving successful.

"If you fail on a question for constitutional referendum, it is never resurrected," he told the ABC's Insiders program.

"I don't want this to fail."

Instead, the Government will put forward legislation to create an Indigenous voice to government. Mr Wyatt said it was his "aspiration" for that bill to pass Parliament in this term of government.

Last year, Indigenous leaders Marcia Langton and Tom Calma were appointed to lead a group to design a model for an Indigenous advisory body.

That report has now been delivered to the Government, with the Minister describing it as "very comprehensive".

"The regional and local bodies have been extremely impressed with the work they have done, because they appointed people with contrasting views, including those strongly supportive of the Uluru Statement," Mr Wyatt said.

Linda Burney, Shadow Minister for Indigenous Australians, said her party remained committed to enshrining a voice in the constitution. She called for any legislation to include a timeframe for achieving that.

"The Government, and the Prime Minister, has the opportunity still in front of it to leave one of the most astounding legacies any prime minister could, and I can't understand why he is being so stubborn in that," she told Insiders.

Disappointment over Senate's refusal to fly Aboriginal and Torres Strait Islander flags

Ms Burney was disappointed with the Senate's decision earlier in the week to vote down a motion to fly the Aboriginal and Torres Strait Islander flags in the chamber, alongside the Australian flag.

Ms Burney, a former state politician in New South Wales, argued the flags had been displayed inside the state parliament for many years.

"We have in this country a remarkable story of 65,000 years," she said.

"Everyone should be proud of that, and that's what anthems and that's what flags help us do."

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The motion was moved by Labor and the Greens, and was defeated by just one vote after the Coalition said it did not support the idea.

Mr Wyatt, a member of the House of Representatives, said it was an issue for the Senate, but added he would rather see the flags displayed permanently outside the building rather than just during special events such as NAIDOC week.

"I'm proud of the Australian flag, but I am as equally proud of the Aboriginal flag because it represents what we fought for, what we have obtained and what unites us," he said.