New Zealand police are searching for eight people still missing after Cyclone Gabrielle struck two weeks ago, amid warnings of more severe weather for the nation's North Island.

The storm hit the island's northern region on 12 February and then battered the east coast, leaving at least 11 dead and displacing thousands.

"The remaining number of people includes those who, for a variety of reasons, do not engage with authorities," New Zealand police said

"Regardless, getting in touch with those remaining eight remains a priority for police, and our staff are exploring all avenues to try and locate them."

More than 6,000 were missing in the immediate aftermath of the storm with communications disrupted in many areas, but that number has fallen in the wake of recovery efforts.

Severe weather again hit the North Island on Friday, with heavy rain prompting more evacuations in Hawke's Bay, one of the regions hardest hit by Gabrielle.

Storms triggered flash floods and evacuation warnings in and around Auckland, the nation's largest city with a population of around 1.6 million.

New Zealand weather forecaster Met Service warned that more storms are possible, especially across the North Island and the top of the South Island.

The emergency agency for Auckland warned city residents to get ready for more rain, predicted to hit in the evening.

"The risk of thunderstorms and localised downpours over parts of the country increases tomorrow," Met Service said.

The forecaster added that it was possible that two tropical cyclones would develop in the week ahead but said: "At this stage, the risk of either directly impacting New Zealand is relatively low".