"He doesn't want to answer any questions about this tragedy," Bob Palmer said. "He just wants to basically acknowledge the support extended over here. John, Vanessa and his family are devastated by the tragic events which resulted in the loss of a loving wife, mother and sister.
"John and his family have been overwhelmed by the support and love extended them by the greater New Zealand police family. Our sincere thanks also go to the New Zealand High Commissioner and his team at Rarotonga for their support.
"The support from the Rarotongan community and John and Vanessa's friends and family has been outstanding and is a great comfort to us all as we deal with this tragedy."
The wedding was postponed. It is expected the bodies will be brought back to Auckland for funeral services.
It is understood Mr Groves' wife, Mary, is also in Rarotonga.
Locals recovered the bodies from the lagoon, near where the group were staying for the wedding, about an hour after the pair drowned.
Mr Palmer has been a police officer for almost 47 years, mostly in Auckland. He is the only remaining chief inspector in New Zealand.
Auckland City district commander Superintendent Mike Clement said the double tragedy had hit Mr Palmer and his wider family "hard".
"We are all reeling from the news and can only imagine the magnitude of the devastation John, his family and the Groves family are feeling," Mr Clement said.
"I know personally that the trip to Rarotonga for Vanessa's wedding was to be the highlight of the year for John and Judy and that much planning and anticipation surrounded it.
"I and Commissioner Peter Marshall have spoken with John on several occasions in the past 24 hours and have offered our absolute support and assistance to help him, his daughter and their friends through this very distressing time."
