The death toll is expected to rise, with British nationals feared to be among those missing.
“No signs of life have been seen at any point,” police said.
“It is now clear there were two groups on the island,” prime minister Jacinda Ardern said at a Tuesday morning press conference. “Those who were able to be evacuated, and those who were close to the eruption.
“We can confirm that among those currently listed as missing or injured are New Zealanders who were part of the tour operation, and tourists from Australia, the United States, the UK, China and Malaysia. That is to the best of our knowledge.”
Two British women are among those injured and receiving treatment in hospital, the UK high commissioner to New Zealand, Laura Clarke, has said.
Australian prime minister, Scott Morrison, said on Tuesday three Australians were feared to be among the confirmed fatalities, with 13 among the injured.
Top officers had said earlier Monday it was too dangerous for emergency workers to search the unstable island for survivors.
About 50 people, New Zealanders as well as foreign tourists, were feared to have been nearby and several were seen near the rim of the crater minutes before the eruption.
Deputy commissioner John Tims said New Zealanders and overseas tourists were among the dead, missing and wounded, and that most of the 18 who survived were injured, including some who were severely burned.
One tourist said he had been on the crater just minutes before the explosion.
“My family and I had gotten off it 20 minutes before, were waiting at our boat about to leave when we saw it,” he said on Twitter.
Many day tours visit the island regularly, and one from the Ovation of the Seas cruise liner was there at the time.
Tour operators took some people off the island before it was declared unsafe. Twenty-three people were rescued, police said, adding that others were still on the island at the time.
My god, White Island volcano in New Zealand erupted today for first time since 2001. 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. #whiteisland pic.twitter.com/QJwWi12Tvt— Michael Schade (@sch)December 9, 2019
In a statement, New Zealand police said: “The Police Eagle helicopter, rescue helicopter, and NZDF aircraft have undertaken a number of aerial reconnaissance flights over the island since the eruption.
“No signs of life have been seen at any point. Police believe that anyone who could have been taken from the island alive was rescued at the time of the evacuation.
“Based on the information we have, we do not believe there are any survivors on the island.
“[We are] working urgently to confirm the exact number of those who have died, further to the five confirmed deceased already.”
A spokesman for the UK's Foreign and Commonwealth Office (FCO) said they were seeking further information about missing British nationals.
Experts said they believed the island, which is New Zealand’s most continuously active volcano, had been dangerous for some time. It last erupted three years ago.
“White Island has been a disaster waiting to happen for many years,” said Ray Cas, a professor emeritus at Monash University, in comments published by the Australian Science Media Centre.
“Having visited it twice, I have always felt that it was too dangerous to allow the daily tour groups that visit the uninhabited island volcano by boat and helicopter.”
Monday’s was the first deadly eruption on White Island, also known as Whakaari, since 1914.
The volcanic island is uninhabited and privately owned. It lies about 50km off the coast of North Island and about 70 per cent of it is under the ocean’s surface.
Additional reporting by agencies