New Zealand's prime minister on Sunday warned residents to hunker down and prepare an evacuation plan as a cyclone began pummelling the northern tip of the country.

Cyclone Gabrielle is forecast to envelop the upper half of the North Island over a 48-hour period from Sunday evening, two weeks after parts of the same region experienced devastating flooding.

Auckland remains under a state of emergency after flash floods swamped the city on January 27, resulting in four deaths and forcing thousands from their homes.

Debris from that deluge remains on the streets of the country's biggest city, which now faces another bout of heavy rainfall and severe winds.

Prime Minister Chris Hipkins said everyone should be ready to face the threats posed by flooding, huge ocean swells and strong winds.

"Our main message to people across the country is to please take the severe weather warning seriously and to make sure you're prepared," he told journalists.

"Make sure you've got your grab-and-go kits, make sure you know where you need to go in the event you need to evacuate your homes."

The MetService weather bureau measured wind gusts of up to 140 kilometres per hour (86 miles per hour) in northern New Zealand on Sunday morning.

"This system poses a very high risk of extreme, impactful, and unprecedented weather over many regions of the North Island from Sunday to Tuesday," the MetService said.

The cyclone is forecast to weaken slightly as it moves slowly south on Monday and Tuesday.

Strong winds forced the closure of Auckland's Harbour Bridge on Sunday, while most flights into and out of Auckland Airport on Monday have already been cancelled.

Gabrielle was downgraded from a tropical cyclone as it approached New Zealand, meaning wind speeds and rainfall would be slightly less intense.

The storm passed over Australia's remote Norfolk Island on Saturday night, where there were reports of downed trees and power cuts but no significant damage.