Middlemore Foundation chief executive Sandra Geange said the money would in particular be helpful for getting additional ultrasound and skin-graft equipment.
"The burns unit put through a year's work in a single day, so at the moment there's no ceiling at what is needed. And it will go on, because it's not a short-term fix," she said.
"There's a great need at the moment."
Perrett said the victims faced lengthy recoveries.
"There will be repeated trips to theatre and a long stay in hospital, during which time patients may face physical and geographic isolation."
In a statement, Health Minister David Clark said the Government was now considering extra money to help the hospital and the victims.
"Additional funding to support Counties Manukau DHB's care of Whakaari/White Island patients is certainly something the Government will be looking at," he said.
DHB chairman Mark Gosche said calls for donations didn't reflect a funding problem.
"It just reflects what people want to do. Lots of people are wanting to help and donate," he said.
"It's just that people want to help and clearly we've never experienced an event of this nature for the National Burns Service."
Geange said the Middlemore Foundation – which runs independently of the hospital's board – had been collecting money for the hospital and burns unit for 20 years and was similar to others around the country.
"Sometimes it's just to close the gap between what the Government provides and what is actually needed," she said