The ship, Braveheart, has been carrying around a marine science team around the Matthew and Hunter islands.
The uninhabited islands have been claimed by both Vanuatu and France since 1976, when France annexed them for New Caledonia ahead of Vanuatu being granted independence.
Vanuatu's prime minister, Charlot Salwai, said that the New Zealand team had asked the government in New Caledonia if it could carry out research, but not Vanuatu.
He said the ship was in Vanuatu's waters illegally.
