A proposed truth and justice commission to aid Indigenous reconciliation will go under the parliamentary microscope.
The Greens have pushed the government to move on enacting other elements of the Uluru statement after the failure of the voice referendum.
The Uluru Statement from the Heart from Indigenous leaders in 2017 called for a truth telling commission and a treaty.
Labor has been largely silent on how it plans to implement the rest of the statement after the referendum to enshrine an Indigenous advisory body in the constitution failed.
The government on Thursday supported the Greens push to send the minor party's private members bill to a parliamentary inquiry.
But the coalition opposed scrutinising the bill, saying the push for a truth telling commission wasn't consistent with the vote of the Australian people.
"This house should be focused on delivering real outcomes for our most marginalised people", Liberal senator Jonno Duniam said.
