A volcanic island in New Zealand erupted on Monday in a tower of ash and steam while dozens of tourists were exploring the moon-like surface, killing five people and leaving many more missing.

Police said the site was still too dangerous hours later for rescuers to search for the missing.

Police Deputy Commissioner John Tims said the number of missing was in the double digits but he couldn't confirm an exact number. He said there were fewer than 50 people on the island when it erupted and 23 had been taken off, including the five dead.

Tims said experts had told them the island remained unstable but search and rescue teams wanted to get back as quickly as they could. He said there had been no contact with any of those who were missing.

He said both New Zealanders and overseas tourists were among those who were dead, missing or injured. He said most of the 18 who survived were injured and some had suffered severe burns.

Some of those involved were tourists from the Royal Caribbean International cruise ship Ovation of the Seas.

"A number of our guests were touring the island today,” the company said. "We will offer all possible assistance to our guests and local authorities. Please keep all those affected in your prayers.

The cruise ship, which had left from Sydney last week, was scheduled to sail to the capital Wellington on Monday night but the company said it would instead remain in the Tauranga port overnight until it learned more on the situation.

"My god," wrote Michael Schade on Twitter as he posted video of the eruption. "My family and I had gotten off it 20 minutes before, were waiting at our boat about to leave when we saw it. Boat ride home tending to people our boat rescued was indescribable."

His video showed a wall of ash and steam around the island and helicopters badly damaged and covered in ash. He said one woman was badly injured but seemed strong by the end.

Prime Minister Jacinda Ardern traveled to the region late Monday. She said the incident was very "significant."

"All our thoughts are with those affected," she said.

Australian Prime Minister Scott Morrison said he'd offered Ardern his support.

"Australians have been caught up in this terrible event and we are working to determine their well-being," Morrison wrote on Twitter.

Brad Scott, a volcanologist with research group GNS Science, said the eruption sent a plume of steam and ash about 3,660 metres into the air. He said it had also affected the whole of the White Island crater floor.

The GeoNet agency, which monitors volcanoes and earthquakes in New Zealand, raised the alert level on White Island from one to two on Nov 18, noting an increase in the amount of sulfur dioxide gas, which originates from magma deep in the volcano.

It also said at the time that over the previous weeks, the volcanic tremor had increased from weak to moderate strength.

Scott said the alert level was often raised and then later dropped again without any eruption. He said there hadn't been any major incidents with tourists visiting the island in the past, although there had been some close calls.

Scott said it was not for him to say whether the island was safe enough to host tourists immediately before Monday's eruption.

Ardern said the focus remained on the search and rescue mission for now and questions about whether tourists should be visiting would be addressed later.

GeoNet at first raised its alert level to four, on a scale where five represents a major eruption. It later dropped the alert level back down to three. Scott said that was because the eruption wasn't sustained beyond the initial blast.

"In the scheme of things, for volcanic eruptions, it is not large,” said Ken Gledhill from GeoNet. "But if you were close to that, it is not good.

White Island is northeast of the town of Tauranga on North Island, one of New Zealand's two main islands.

Experts say it's New Zealand's most active cone volcano and about 70 per cent of the volcano lies under the sea.

Twelve people were killed on the island in 1914 when it was being mined for sulfur. Part of a crater wall collapsed and a landslide destroyed the miners' village and the mine itself.

The remains of buildings from another mining enterprise in the 1920s are now a tourist attraction, according to GeoNet. The island became a private scenic reserve in 1953, and daily tours allow more than 10,000 people to visit the volcano every year.

The island is also known by the indigenous Maori name Whakaari.