Conservation Minister Maggie Barry says if Ngapuhi leader Sonny Tau can expect to face legal consequences if he is found to have broken the law after being found with several protected kereru.
Ms Barry said the Department of Conservation was giving priority to the investigation, now in its third week, but it was "complex."
She had not been briefed on the details of it and would not expect that to happen until it was complete.
"We need to be very careful to ensure we can find and track all the activities, peel away the anecdotal, and get to and stick with the fact. Once we have those we will certainly take action."
She said any kind of predation on endangered species was illegal under the Wildlife Act and is not to be tolerated. "Be absolutely clear if somebody - anybody - is found to have transgressed the law, they will face the full consequences of breaking the law."
She would not reveal any of the circumstances of the case, such as how Mr Tau came to be in possession of the kereru.
Mr Tau has admitted in a statement that a Doc officer had spoken to him about kereru he was found with at Invercargill airport and said it was a mistake that he deeply regretted.
He has refused to comment further while the investigation was underway, but said he was cooperating with Doc.
On Monday, Ngapuhi's Treaty settlement body, Tuhoronuku, voted to stand down Mr Tau as chair although he remains on the board.
The Ngapuhi iwi runanga also decided to keep him on as its chair, citing his 15 years of service.
Labour MP Kelvin Davis has called on Mr Tau to stand down from all his iwi roles and seek re-election to ensure he still had the mandate of his people.