Most of the victims were tourists and around 20 people remain in hospital with severe burns.
New Zealand police confirmed the 16th victim died on Saturday at Sydney’s Concord Hospital, one of several Australian hospitals where survivors suffering from severe burns were being treated.
Police released the names of three further victims on Sunday, including US citizens Matthew, 13, and Berend Hollander, 16, who lived in Australia and Australian Karla Matthews, 32.
Five other victims have been named, four of whom are Australians.
The first to be named was Krystal Browitt, a veterinary nursing student from Melbourne, Australia, who turned 21 on November 29.
On Sunday, Zoe Hosking, 15, and her stepfather Gavin Dallow, 53, both from Adelaide, were confirmed as dead. Lisa Dallow, Zoe’s mother, is being treated for severe burns.
Anthony Langford, 51, of Sydney, has also been confirmed dead. He was travelling with his wife Kristine Langford and their children Jesse, 19, and Winona, 17.
Jesse survived the eruption and was identified in a New Zealand hospital on Tuesday evening. His mother and sister are still unaccounted for.
The fourth person identified on Sunday is New Zealand resident Tipene Maangi, 24.
A search failed to locate the bodies of the last two victims of the eruption on Sunday.
Two four-person teams landed on the volcanic White Island by helicopter early on Sunday and searched a location thought to be where one of the bodies might be.
The teams were wearing heavy protective clothing due to the toxic air and gases present on the island as a result of the eruption.
New Zealand Police national operations commander John Tims said the search will continue on Monday.
"The divers continued their work in the water off the island today. This is a difficult and ongoing task," he said.
"While it is frustrating not to have located the remaining two bodies, I’d like to reiterate our commitment to doing all we can to provide a sense of closure to the grieving families."
Mr Tims said the process of identifying victims and releasing bodies to their loved ones was ongoing in Auckland, New Zealand’s largest city.
“We will continue to release the names of those who have died as soon as we are able to,” he said.
Two British women were among those admitted to hospital in New Zealand after the volcano erupted.
All 13 Australians who suffered burns were transported to hospitals around Australia for treatment, at least eight of whom are reported to be in a critical condition.