The Greens introduced a private member's bill in the Senate to establish such a commission as it tries to push the government to act on the rest of the Uluru statement.
It wasn't just governments that were responsible for truth-telling, Ms Burney said, as she noted that states and territories were also working on the issue.
Linda Burney says the federal government is committed to a truth-telling commission. (Michael Errey/AAP PHOTOS)
"Labor is still very committed to the issues of truth-telling and we're working very closely with states and territories," she told ABC radio on Tuesday.
"The issue of truth-telling is something that I'm seeing right across the country being done in a variety of ways.
"It's not just governments that are responsible for this, it is also communities that are taking it up with gusto."
She said she didn't feel that Indigenous affairs remained a bipartisan issue, calling the coalition "spoilers" after they failed to support a voice to parliament.
The referendum's result was "heartbreaking" but the silver lining was that some 6.5 million Australians voted 'yes' and there had been an emergence of young Indigenous leadership, Ms Burney said.
"Also, of course, the issue of Aboriginal disparity and disadvantage and the shocking statistics that are around Aboriginal wellbeing were on the national stage and that's a good thing," she added.
"I take those silver linings as really positive outcomes."
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