Indigenous Affairs Minister Ken Wyatt wants to achieve political consensus on constitutional recognition and a voice to parliament.
Mr Wyatt has asked Labor, One Nation, the Greens and independent politicians to join a new parliamentary working group on indigenous issues.
But the group isn't a formal committee and won't have any decision-making powers.
It won't report to the House of Representatives or the Senate.
"Achieving constitutional recognition of indigenous Australians, refreshing Closing the Gap, fostering an environment for truth-telling and ensuring that indigenous voices are heard by governments are all priorities of ours," the minister wrote in his letter to the parties.
"I look forward to working with you and all those across the parliament, to achieve Iong-lasting positive outcomes for all indigenous Australians and our nation."
Members of the group will be decided by Friday, ahead of its first meeting slated for parliament's final sitting fortnight of the year.
Mr Wyatt will lead the group and will be joined by seven government members, five Labor and two independents along with one representative each from the Greens, One Nation and Centre Alliance.
The minister will also outline plans for how an indigenous voice to parliament would work in coming days.
It comes as Labor senator Pat Dodson condemned Prime Minister Scott Morrison for not attending events at Uluru at the weekend to mark the anniversary of it being handed back to traditional owners and the closure of the climb.
"He's ducked us, the prime minister, and that's a real insult to people who hold and carry customary law," Senator Dodson told the ABC.
Mr Morrison missed the opportunity to highlight the importance of the climbing ban for indigenous Australians, he added.
Environment Minister Sussan Ley attended Uluru as the sole representative of the federal government.
Senator Dodson was one of four Labor representatives who attended, including two other indigenous members, Linda Burney and Malarndirri McCarthy.
Labor leader Anthony Albanese did not attend.
Australian Associated Press