New Zealand police on Tuesday announced an investigation into how an eruption at the White Island volcano led to an estimated 13 deaths.

The threat level at the volcano was raised in the week before Monday's disaster, prompting questions about whether tour groups should have been allowed to visit the popular destination off the North Island coast.

Police said in a statement that they "commenced an investigation into the circumstances of the deaths and injuries" at the volcano.

However, they backed away from an earlier announcement that the probe was a criminal investigation, saying instead it was being carried out on behalf of the coroner.

No reason for the reversal was immediately provided.

The investigation would run parallel to a probe conducted by the workplace watchdog Work Safety New Zealand.

Officials have confirmed five fatalities and say another eight are missing presumed dead after New Zealand's most active volcano exploded while tourists were exploring it on Monday afternoon.

Speaking before the investigation was announced, travel operator White Island Tours said it took safety responsibilities extremely seriously.

"We take our steer from (government geoscience agency) GNS, who send us a report telling us what the activity levels are, if it's deemed level two, which it was yesterday," chairman Paul Quinn told TVNZ.

Quinn said the company had taken visitors to White Island when the activity alert was at level two, which warns of "moderate to heightened volcanic unrest".

He said two of the company's guides were unaccounted for after the eruption.