Senator Jacinta Nampijinpa Price has revealed why she thinks Labor shouldn’t support Greens proposed bill to establish a Truth and Justice Commission.

The proposed bill follows the failure of Labor's Voice to Parliament referendum, which saw 60 per cent of the nation vote against the Voice.

“Labor in their right mind shouldn’t be supporting it because they clearly understand the result of the referendum,” Ms Price said.

“It would not help benefit them to support this, but you never know in desperation they may choose to do say.”