A family of four, including two children, were killed in a landslide late Wednesday after becoming trapped in their home at a village in the island's western Ba region, the information ministry said.
It said almost 3,500 people had been forced from their homes by the torrential downpour that has continued since the weekend, and a state of natural disaster has been declared in the worst-hit areas of the west.
No further details of the landslide victims were available.
Earlier this week, two farmers were killed in separate incidents as they tried to protect their livestock from rising waters.
The government said roads had been cut and some communities were without power and water supplies, advising people to avoid low-lying areas and take precautions against water-borne illnesses.
New Zealand Foreign Minister Murray McCully announced an initial NZ$350,000 ($286,000) for flood-relief efforts and said further aid was being considered.
"New Zealand is coordinating closely with authorities and relief agencies on the ground, as well as with Australia and France," he said.