A family spokeswoman, who is a close relative of the children's 22-year-old mother, said they had almost sold out a raffle as the first step in their fundraising effort.
"The children's parents are staying in a motel and we want to help them with the costs of that," she said.
"We hope to raise enough to provide something for the little ones when they recover."
Steps are being taken to set up a bank account for people to make donations.
Several close family members are also in Auckland, helping to support the parents.
"We are taking turns to be with Manaia and Rious, to give their mum and dad a break," the family spokeswoman said.
"Their mum is not getting much sleep.
"We are all waiting for the children to wake up," she said.
"At this stage they seem to be getting on really good."
Manaia and Rious remain sedated as part of their initial treatment.
Their surgeon indicated last week that patients like them are managed in intensive care for at least two weeks, and maintained at a stable level.
Consultant burns and plastic surgeon Amber Moazzam said the children would be transferred to the national burns unit across the corridor from the ICU where they are now, once their initial treatment is complete.
The family spokeswoman said it was their intention to make a donation to the hospital from their appeal.
"If we raise enough money, we will donate some of it to the burns centre."
- The Gisborne Herald