Rescuers have been unable to access the island, which is covered in grey ash.
The volcano vent continues to emit steam and New Zealand's geoscience agency has warned on another eruption in the coming 24 hours, with 50-50 chances.
New Zealand's Prime Minister Jacinda Ardern has expressed "unfathomable grief" after the volcanic eruption have claimed 13 lives.
Ardern confirmed five fatalities and said another eight people were still missing after Monday's tragedy at White Island.
There was little hope of finding the missing alive, after overnight aerial reconnaissance flights found no signs of life.
"The focus this morning is on recovery and ensuring police can do that safely," she told a press conference.
Among those on the island during the cataclysm were tourists from Australia, the United States, Britain, China and Malaysia, as well as their New Zealand guides.
"To those who have lost or are missing family and friends, we share in your unfathomable grief and your sorrow," Ardern said.
"Your loved ones stood alongside Kiwis who were hosting you here and we grieve with you."
Ardern singled out "our Australian family" for sympathy, while her Australian counterpart Scott Morrison warned his compatriots to brace for "a very hard day".
Morrison said there were fears that three of the five dead were Australian, and another eight citizens were unaccounted for.
He described the tragedy as a "time of great innocence and joy interrupted by the horror of that eruption".
"This is a very, very hard day for a lot of Australian families whose loved ones have been caught up in this terrible, tragedy," he told reporters in Sydney.
A total of 31 people — including 13 Australians — were in hospital with various injuries, some listed as critical with serious burns.
White Island Tours, a trip operator, confirmed that two of its guides were unaccounted for, while Britain's high commissioner in Wellington said two female citizens were hospitalised.
Concerns about further eruptions, poisonous gases and choking ash stalled efforts to recover bodies.
"We will only go to the island when it is safe to do so for our people," police spokesman Bruce Bird said.
He said a helicopter scoured the area for 45 minutes, checking if anyone was still alive -- without success.