HNZ regional manager Neil Adams said he hoped the family would be rehoused soon.
"We'll continue to work with them to find a more permanent home."
Adams said the Fire Service was investigating the cause of the fire.
"The Fire Service has told us the fire's area of origin is at the foot of the corner of a bed in one of the children's bedrooms."
Fapiano (left) and Mafi Lemeki with goods donated by the Beachhaven Community. Photo/Jason Oxenham
Meanwhile, as the Lemeki family waits for HNZ to find them a new home, the Beach Haven community has rallied to do what they could to replace the family's charred belongings.
After a call for help was put out on a local Facebook community page, donations began flooding into the Birkdale Community House.
A shed out the back and a small room have been filled with boxes of blankets, children's toys, bikes, kitchen appliances and a new washing machine.
Birkdale Beach Haven community project manager Carla Van Walen said it was "wonderful to see the community wrapping their arms around a family in need".
Speaking about the community's love towards her family was the one thing that moved Mafi Lemeki to tears.
"We are lucky we have the lovely community, they sorted us out. I'm happy at the love."
Asked what other goods her family might need, Lemeki said just a home in Beach Haven.
"Our house to come, we want to be back in Beach Haven. I want to be in this community."