Indigenous Australians Minister Ken Wyatt faces growing concerns in the Coalition party room over calls to create a "first Australians voice" to Federal Parliament in a new power to be written into the constitution.

But Indigenous leaders stepped up their support for the reform after Mr Wyatt vowed to take the question to the Australian people in a referendum during this term of Parliament - a timetable backed by Labor.

Liberals warned against amending the constitution to set up the new "voice" when the idea had already been rejected by former prime minister Malcolm Turnbull's cabinet two years ago, highlighting the challenge for Mr Wyatt in gaining a consensus inside the government.

"There are huge inflated expectations that are just not realistic," said one MP, in a view echoed by others.

Mr Wyatt set out his plan in a major address on Wednesday that set the timetable for the referendum but hedged on the wording to be inserted into the constitution to recognise Indigenous Australians and give them a greater voice in national affairs.

His position does not guarantee the key objective set out by Indigenous leaders in the Uluru Statement two years ago, which called for a "First Nations Voice enshrined in the constitution".

Labor's Indigenous affairs spokeswoman Linda Burney said her party backed the Uluru Statement "wholly" and wanted the voice to be entrenched in the constitution, setting up an impasse with some members of the Coalition who claim the idea could establish an unacceptable "third chamber" of Parliament.

Speaking after his address, Mr Wyatt said he would be "pragmatic" about the precise change to be put to the Australian people.

"It's about what will be acceptable in a referenda process that people will acceptable and the states and territories will accept - and we cannot afford to let it fail," he said.

Prime Minister Scott Morrison has called for a bipartisan approach to the reform without putting any preconditions on the model.

NSW Liberal senator Andrew Bragg backed Mr Wyatt's plan on Wednesday as a sign of the "serious engagement" with Indigenous Australians.

"The government is extending a hand to the Indigenous community. As the minister said, any model would need to win the support of both the Indigenous community and middle Australia so that is a good start," Senator Bragg said.

While a parliamentary committee issued a bipartisan call last November for a "co-design" approach to consult on the reform with the community, the inquiry included additional comments by Queensland Liberal senator Amanda Stoker that carry influence with conservatives within the party room.

"I maintain a scepticism of some of the proposals for constitutional recognition," Senator Stoker wrote, adding there was an "absence of a consensus" among Indigenous communities about the change.

Senator Stoker told The Sydney Morning Herald and The Age on Wednesday that she backed moves to take discrimination against Indigenous Australians out of the constitution but did not support writing special powers for one group into the nation's founding document.

"If it is some form of grand gesture or a proposal for a third chamber, that is going to be a lot more complex," she said.

"It really does depend wildly on what the model looks like.

"If we're doing this to satisfy a particular part of the Australian community then let's work out what they've got in mind, because at the time of the committee last year they didn't know."

Victorian Liberal senator James Paterson expressed a similar concern.

"I will carefully consider any formal proposal for constitutional recognition, but any change that threatens our successful parliamentary system or one which treats Australians differently based on their race would be a backward step," he said.

Liberal MP Tim Wilson said there was "enormous goodwill" for a structured voice to the nation but that this frayed when the focus turned to changing the constitution.

"There is a misdiagnosis that credibility for a voice comes from a constitutional anchor, when it's credibility would come from connection to community and country," Mr Wilson said.

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While the principle of Indigenous recognition has bipartisan support and Labor has pledged to work with the government, the concerns in the Coalition party room could make it impossible to create a voice in the constitution.

In one scenario, this could lead the government to recognise Indigenous Australians in the constitution but use legislation to establish the voice to Parliament - an option Indigenous leaders regard as too weak but one Mr Wyatt has not ruled out.

Former deputy prime minister Barnaby Joyce, a member of cabinet when it rejected the Uluru Statement two years ago, repeated his concerns on Wednesday about the Indigenous voice being a "third chamber" of Parliament.

He said a new Senate voting system would be a better way to give indigenous Australians real power.

Mr Joyce said the current Senate voting system could be changed to allocate seats by region rather than by state, creating more opportunities for people outside the major cities.

"You would have a vastly increased chance of electing Indigenous Australians who would have real and actual power," he said.

"Overwhelmingly, many of those senators from outside the capital cities would be Aboriginal."

In an influential warning for some Liberals and Nationals, the Institute of Public Affairs warned against the changes on Wednesday.

"Proposals to insert race into our nation's founding document are radical, illiberal, and a violation of all principles of racial equality. Race has no place in Australia's Constitution," said IPA research director Daniel Wild.