Continuing volcanic activity since Monday’s eruption has prevented rescue services going to the island.
But police said in a press conference on Thursday the site was expected to be stable enough to allow the planned retrieval operation to proceed, although New Zealand’s seismic monitoring agency said a further eruption remained a possibility.
New Zealand Prime Minister Jacinda Ardern said: “Everyone is desperate to get those victims back and so I know that will be a matter that the police are utterly focused on.”
That number does not include those left on the island.
A total of 47 people were on White Island, New Zealand’s most active volcano, when the eruption occurred, including two British women who were among those admitted to hospital.
No details of their condition were available on Thursday.
Deputy Commissioner Mike Clement of New Zealand Police explained the recovery operation: "There is not a zero-risk with regard to this plan. It does come with risk.
"Shortly after first light tomorrow [Friday] NZDF (New Zealand Defence Force) assets, people and capability will deploy to the island, assisted by specialist capabilities from across other agencies, including New Zealand police.
"They will go onto the island and they will make every effort to recover all of the bodies from the island and return them to the Wellington (ship). And from there, we will move those bodies back to the mainland."
Relatives of victims on the island have been frustrated that their bodies have not been recovered sooner.
"It's not frustration that they can't get to the island, it's more frustration that they haven't gone to island," said Mark Inman whose brother, tour guide Hayden Marshall-Inman is missing.
"There's been two perfect opportunities to get out there and they haven't gone - red tape, bureaucracy, leadership has failed.
"We're trusting experts that sit behind a desk, making calls based on statistics when you've got two pilots and a bunch of volunteers who go to the island every, single day and know the island inside out, saying 'let's go, let's do it, let's get it done'."
The perceived delay in rescue services attending the island is due to the fear over further eruptions.
New Zealand’s GeoNet seismic monitoring agency on Thursday lowered White Island’s volcanic alert level to two, noting there had been no eruption since Monday, when the level had briefly been raised to four. Its alert level since late on Monday had been three on a scale where five signifies a major eruption.
A further eruption in the following 24 hours was still a possibility, the agency said, noting volcanic tremors were rising, with steam and mud being vented regularly.
Authorities said those on the island at the time also included 24 Australians, nine Americans, five New Zealanders, four Germans, two Chinese and a Malaysian.
Dozens of people were severely burnt in the eruption, with volcanologists speculating many may have been hit by fierce jets of scalding steam bursting laterally from the volcano.
The two people who died overnight were Sydney brothers Berend and Matthew Hollander, aged 16 and 13. Their parents Martin and Barbara were among those listed as missing on Thursday.
Those now confirmed to have died, or who are missing presumed dead, include a mother and her 20-year-old daughter from Brisbane, and an Adelaide man and his step-daughter, whose mother was being treated in hospital.
A total of 19 victims were still being treated on Thursday in intensive care and burns units at several hospitals across New Zealand. A further seven have been flown to Australian hospitals.
The enormity of the task confronting the several hospitals treating survivors was made clear when medical officials said extra skin had been ordered from American skin banks.
Dr Peter Watson, chief medical officer from the Counties Manukau’s district health board, said hospital personnel anticipated needing an extra 120 square metres of skin for grafting operations.
White Island is the tip of a mostly under-sea volcano 30 miles off New Zealand’s North Island and has been a popular attraction visited by thousands of tourists each year.