Judge Damian Stone is considering the request and has given the Crown until the end of Monday to reply.
The Māori health authority was set up last year under health reforms, with the aim of giving Māori a greater say in their own healthcare and ending poorer health statistics.
In their Statement of Claim lodged with the tribunal, Lady Tureiti and Kuka said disestablishing the authority would likely prejudicially affect Māori.
There would no longer be a Māori body which aimed to create services to achieve the best possible health outcomes for Māori and promote Māori health.
They pointed out historic underfunding by the crown for Māori health providers and primary health organisations (umbrella groups comprising GP practices and other community health services).
The Crown was supposed to work with Māori to change that, but had not, they said.
Abolishing the authority would be inconsistent with the Treaty principles of tino rangatiratanga, partnership and equity, the claim said.
There is another claim for an urgent Tribunal hearing regarding the Government’s 100-day plans.
Tauranga-based iwi Ngāi Te Rangi is accusing it of breaching the Treaty by failing to protect Te Reo Māori.
