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.

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