One patient has already left Wellington for Australia on a private plane.
Gavin Dallow's stepdaughter, 15-year-old Zoe Hosking, is also presumed dead on White Island.
Residents in surrounding areas are in danger and must leave immediately, authorities say.
The nine-year, $496 million deal has the highest annual salary of any contract.
In July, a water main break saw an estimated 800,000 litres of wastewater flow into the lake.
1 NEWS' Katie Bradford says Grant Robertson has failed to identify a single 'shovel ready' project.
Despite key ingredients being imported, the company claimed their products were locally made.
The Grammy winner faces felony charges over the August 2018 brawl.