The administrator of the Papua New Guinea province of Bougainville, Peter Tsiamalili, says he is disappointed that police personnel from New Zealand left the island without informing the local administration of their decision to leave.
Mr Tsaimalili told The National newspaper he should have been told about their departure.
Commenting on the death threat that made them leave the island, Mr Tsiamalili said threats on Bougainville are a daily occurrence and there was no course to be alarmed at.
He says in such situations they should talk to the Assistant Police Commissioner before leaving.
He said the Bougainville administration is responsible for the welfare and life of all citizens on the island, including visitors regardless of where they come from.
New Zealand police won't return for the time being, saying the immunity status is no longer clear.
Earlier, the New Zealand foreign minister said it was no issue because the New Zealand police were covered by the agreement applying to the United Nations.