Ishmael Kalsakau made the statement over two southern islands - Matthew and Hunter - during the visit last week of the French President Emmanual Macron.
The two islands are held by New Caledonia but southern Vanuatu chiefs and politicians say they are sacred to the ni-Vanuatu people.
It comes after four chiefs handed a petition to Macron over the dispute.
The islands are also known as Umaenupne and Leka, and have traditionally been a place to perform religious and customary ceremonies.
In their statement adjoining the petition, the chiefs said the peoples of the islands of Tanna, Aneitym and Futuna hold the two islands in reverence.
"As has been the case for centuries, Matthew and Hunter islands continue to hold a central place in the religious and cultural observances of ni-Vanuatu people," the chiefs said.
They said that for many decades Matthew and Hunter islands have been integral to Vanuatu and therefore cannot understand why France has claimed them.
"Not only France's action torn away a vital part of Vanuatu's territory, they prevent ni-Vanuatu people from visiting the islands to perform religious and customary ceremonies of paramount importance.
"This is specially lamentable because maintaining our people's traditional practices is one of the ways we are combating the legacies of colonial exploitation.
"Matthew and Hunter islands are the rightful inheritance of the people of Vanuatu. But France is depriving them of their patrimony," they said.