Attorney-General Christian Porter has effectively ruled out enshrining an indigenous "voice" to parliament in the constitution.
The federal government is spending $7.3 million consulting on a model for the indigenous voice, which it plans to put to Australian voters in a national referendum.
But Mr Porter has made it clear the voice will not be written into the nation's birth certificate.
"That doesn't mean you don't give full consideration to other plans or models and ways in which you recognise indigenous people in the Australian Constitution," he told Sky News on Tuesday.
"But what we have seen so far from advocates in this area is something which is so vague it is very, very difficult to say whether you are for or against it, because of the fact it is so ill-defined."
The indigenous voice was recommended by about 300 Aboriginal and Torres Strait Islander leaders at Uluru in 2017, but has stalled ever since.
Prime Minister Scott Morrison and his predecessor Malcolm Turnbull have both rejected the idea, claiming it would be nothing more than a "third chamber" of power.
But the government has since agreed to explore the idea with Aboriginal and Torres Strait Islander people.
Labor leader-elect Anthony Albanese said he hoped the government would be "constructive" about changing the constitution.
"We are diminished as a nation when we don't recognise the fact that we have the oldest continuous civilisation on the planet here in Australia - it enriches all of us," Mr Albanese told reporters in Caboolture.
"But we are also all diminished by the fact that they are the most disadvantaged group in our nation.
"Part of that is recognition in the constitution. Part of that is practical steps - how do we close the gap on education, on health, on infant mortality, on drug addition, on incarceration."
