They are believed to have beached early Friday, tvnz.co.nz. reported.
According to Department of Conservation (DOC) spokeswoman Carolyn Smith, only 10 were still alive and they were in poor condition.
Smith said there was little chance of saving the whales with the weather closing in and high tide not until late Friday night.
The DOC said it was a difficult decision to euthanise a group of stranded whales.
The whales' carcasses will be buried, the authorities said.