The Greens will seek to establish an Indigenous truth and justice commission as a prominent elder criticises the government's "silence" following the voice referendum failure.
Legislation will be introduced this week to establish the commission, which would be empowered to examine historic and ongoing injustices against First Nations people and make recommendations to parliament.
"We have been waiting for the opportunity to not just tell our truths but to have Australia deeply listen to our experiences, past and present, as the oldest living culture in the world," Greens senator Dorinda Cox said on Sunday.
The Albanese government has set aside funding to establish a Makarrata Commission which would supervise a truth-telling process.
But little has been publicly outlined about its progress following the defeat of the voice referendum which shook the government and left many Indigenous people traumatised.
Indigenous Affairs Minister Linda Burney on Saturday said funding for the commission was still in the budget.
"The government has been very clear, and I have been very clear, that we will take our time to make sure we get this right," she told reporters.
She said the government was spending billions of dollars on housing, education and jobs for Indigenous Australians and noted that truth-telling was happening at a local and state level and in the community.
"In my view, the process of truth-telling in this country is well and truly underway and it has been underway for a very long time," she said.
Uluru Dialogues chair Pat Anderson said the referendum outcome should not stop the government from enacting the Uluru Statement from the Heart.
"It has been nine months since the referendum and there needs to be forward momentum," she said in a statement reported by the ABC.
"Our people are hurting from the silence, and there needs to be leadership."
Treasurer Jim Chalmers defended the government's efforts to deliver better outcomes for Indigenous people.
"I take Aunty Pat's contributions very seriously," he told reporters.
"I don't feel like we have (been silent). I feel like we've been working away on all of the various ways that the government intends to close the gap."
The voice would have established a permanent consultative committee with Indigenous members to advise the government on matters relating to First Nations people and their wellbeing.
Senator Cox said it was important for Australians to know that in the truth-telling process, "we will begin to heal as a nation".
"The work that we do now must be grounded in our self-determination to chart our pathway forward, to achieve better outcomes for First Nations people," she said.
The private member's bill can easily be defeated in the house because of the government's majority but the topic is politically charged.
Victoria has started its own truth-telling commission amid global moves to give Indigenous people a voice.
South Africa's Truth and Reconciliation Commission, established after in 1995 after the end of apartheid, has been highlighted for addressing the injustices of colonialism and the system of racial segregation and discrimination that followed.