The investigation into the death of Lance Corporal Nicholas Kahotea on Wednesday night continues.
The SAS soldier has links to Tauranga Moana and died after an accident during a training exercise in Auckland at Ardmore.
Age 36, Nicholas is of Ngāti Pukenga and Ngāiterangi descent on his father's side, and is a direct descendant of Taiaho Hori Ngātai.
Taiaho was the only surviving chief of the Battle of Gate Pā that was fought in 1864.
The Defence Force said that Lance Corporal Nicholas Kahotea of the First New Zealand Special Air Service Regiment would be remembered as a professional soldier, a father and friend to many.
The joint training exercise with the United States Army has been suspended as the Police, Defence Force and WorkSafe investigate what happened.
Army Chief Major General John Boswell said Nicholas Kahotea was a "consummate professional", an "outstanding soldier" and a "top bloke", who was known for his dedication and reliability.
"I know that his family, friends and colleagues will be keenly feeling the loss and we offer our deepest condolences."
He joined the Army in 2006 and became an SAS officer eight years later after going through the rigorous training programme.
He served in Afghanistan and was decorated four times. He was awarded the New Zealand Operational Service Medal (NZOSM), New Zealand Defence Service Medal (NZDSM), New Zealand General Service (NZGSM) and NATO ISAF (Afghanistan).
Lance Corporal Kahotea was taken by helicopter to Auckland City Hospital last night but was later pronounced dead.
The large-scale training exercise with the US military was supposed to continue until 23 May.
Acting Defence Minister Winston Peters confirmed to reporters that the exercise had been suspended.
"We pass on our serious condolences to the family and the wider family as well. At this point in time it will obviously be the subject of coronial inquiry and I can't say much more than that."
Details of the incident which led to Lance Corporal Kahotea's death are unclear.
Auckland resident Andi Brotherston saw a very large military-style helicopter landing on the field at Auckland Domain, a few hundred metres from Auckland Hospital, at about 8.15pm. It was met by an ambulance.
Ms Brotherston said she often saw the police Eagle helicopter and the Westpac rescue helicopter landing at the hospital, and she was sure it was neither of those.
"There was a huge black helicopter that was making a lot more noise than the Eagle. It actually circled around and landed in the middle of the rugby field, right beside Auckland Hospital."
A second chopper, which Ms Brotherston said also looked like a Blackhawk military helicopter, circled overhead,
"There was a St John ambulance parked right near the rugby field looking like it was waiting. And I just assumed there'd been some sort of military incident and this big Blackhawk was dropping a patient off."
Auckland Hospital would not comment on the incident but said large helicopters could not land on its helipad and it had an arrangement with the defence force about landing larger choppers.
Third fatality during military training exercises this year
Lance Corporal Kahotea's death is the third to occur during military training exercises this year.
Zachary Christopher Yarwood, 23, died after an incident during an advanced diving course in Devonport in March.
Singaporean soldier Aloysius Pang was crushed between the barrel of an artillery gun and the cabin he was in during a training exercise at Waiouru in January
Former SAS soldier David Moloney said there were inevitably risks during military training exercises, but it was crucial for soldiers to be exposed to the sorts of conditions they may face during combat or other high-pressure situations.
"They will get placed in positions where it will be quite dangerous and you need to be able to react quickly and effectively.
"You know, if you haven't been shot at before, it may be difficult for you. It's to make it as realistic as possible so you'll be as effective as possible when it happens."
Mr Moloney said the tragedy would have hit Lance Corporal Kahotea's fellow troops hard.
Detective Senior Sergeant Malcolm Hassall said police were called at 10pm on Wednesday to investigate the sudden death on behalf of the Coroner.
WorkSafe New Zealand was also informed about the death.
The NZDF confirmed it would hold a Court of Inquiry.