A total of 47 people were on White Island, off the coast of North Island, when the eruption occurred.
He said police were talking with Fire and Emergency NZ and the Defence Force but it would ultimately be his decision about when to return to the island.
The family are among 24 Australians believed to have been on the island at the time of the eruption.
Jessica (left) and Julie (right) Richards have been found dead following the eruption of a volcano in New Zealand.
The bodies of eight more people are believed to be on the island, but it is still too unsafe for the teams of rescuers to travel there and for forensic pathologists, odontologists and other victim identification experts to begin their work.
'We can't because Whakaari is in a state of mourning, her descendants have passed on and they're lying dead, still there on the island.
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New Zealand's Prime Minister Jacinda Ardern addresses the media following an eruption of the White Island volcano, in Whakatane, New Zealand December 10, 2019.
Twenty-seven people have horrific burns to 30% or more of their body and 22 are also on airway support due to the severity of their burns, said medical authorities.
Officials said they are working with disaster specialists and forensic experts to identify the victims so they can be returned to their families. "And the parameters are worsening at the moment", Graham Leonard, a senior volcanologist at GNS Science, told a news conference in Wellington. It also said volcanic tremors had increased from weak to moderate strength.
Martin and Barbara Hollander and their sons Berend and Matthew were on holiday in New Zealand from their northern Sydney home and have not been heard from, although they don't appear on the police missing list.
Two Britons have also been confirmed as injured and Malaysia's High Commission on Wednesday confirmed one of its nationals was critically injured, in addition to one previously announced death.
The first victim to be identified was tour guide Hayden Marshall-Inman, a local of nearby town Whakatane, who has been named by his brother on Facebook.
Rescue teams are still unable to enter the island out of concern that the volcano could erupt again. The alert level was increased further after the eruption, and remains elevated.