Clark said he expects DHBs to meet their Treaty of Waitangi obligations as specified in the New Zealand Public Health and Disability Act 2000.
"I am expecting you to report on progress with how you are meeting these obligations as part of your Annual Plan reporting."
Board member and Ngati Kahungunu iwi chairman Ngahiwi Tomoana said the change would bring a positive outcome to all.
"There is an assumption, or even a phobia, that if Māori win, someone has to lose."
Flood said the statistics spoke for themselves.
"You are not Māori and you won't really understand it from our perspective. I'm not saying that you are a lesser person because you don't understand it. What I am asking is that you trust us ... "
Executive Director of Primary Care Chris Ash said the strategy team were working to find the appropriate wording which correctly reflects the organisation's equity approach.
Bernard Te Paa, HBDHB's executive director of health improvement and equity, said the "proof in the pudding is going to be how this expression is then turned into actions and commitment by this organisation and then the results that we then see that measure that change that we have".
HBDHB chief executive Kevin Snee said the "language could be exclusive if you are not careful".
"You have also got a range of other populations who are critically deprived and suffering poor health needs as well."
All board members reached a consensus they were strongly supportive of equity for everyone with a specific emphasis on Māori.
The executive management team will now discuss how it can be achieved and will report back.