Moriori are calling for the Crown and Ngati Mutunga to give them compensation for the loss of nearly all their land and for the lives of ancestors killed by Taranaki Maori in the 1830s.
Treaty Negotiations Minister Christopher Finlayson talked with Moriori during a visit to the Chatham Islands last week.
Hokotehi Moriori Trust executive chair Shirley King says ever since the Taranaki invasion and colonisation, Moriori have been left behind and have been barely acknowledged by succesive governments.
Ms King says in order to move ahead both the Crown and Maori need to be held accountable.
She says the Maori Land Court helped alienate Moriori from their lands leaving them with less than 3%.
Part of the trust's Treaty claim would include recognition of their tangata whenua status and mana over Rekohu or the Chathams Islands.
Moriori are still seeking a mandate to settle with the Crown.