"Next of kin have been informed and our priority is to provide comfort and support to the family and shipmates."
Minister of Defence Jonathan Coleman extended his condolences to Mr Delamere's family and crewmates.
"The tragic loss of this young life will be a big shock to all those close to William Delamare," Dr Coleman said.
"The NZ Defence Force will be providing support for his whanau and close mates at what is a very difficult time for them."
Labour's defence spokesman Iain Lees-Galloway this would be a difficult time for NZDF personnel.
"My heartfelt sympathy and condolences are with those in Rarotonga and at home who knew ASCS Delamere.
"I want to recognise his contribution and the contribution of all of our servicemen and woman who are often working and living far from their loved ones at home.''
The coroner in Rarotonga is investigating the incident.
The coroner in Rarotonga is investigating the accident.