A state of emergency was declared in Auckland on Friday after torrential rain caused widespread flooding in New Zealand's largest city, closing the airport and forcing the cancellation of an Elton John concert.

Auckland mayor Wayne Brown told a news conference late on Friday he was "deeply saddened" after a body was found in a northern suburb. Police have not confirmed whether the death was a result of the flooding.

Flash floods turned many of Auckland's roads into rivers as the wild weather closed the city's airport, leaving some terminals ankle-deep in water.

Auckland airport, New Zealand's largest, confirmed there would be no domestic or international departures or arrivals before noon local time on Saturday.

New Prime Minister Chris Hipkins, who was sworn in Wednesday after Jacinda Ardern's shock resignation, wrote on Twitter that government agencies were "working flat out" to help.

He said the national crisis management centre, housed under the parliament building in the capital Wellington, was helping coordinate the emergency response.

The persistent downpour also washed out Elton John's concert at Auckland's Mount Smart Stadium amid concerns for crowd safety.

Emergency services were swamped by calls for help as civil defence officials warned residents to stay home.

Police also urged people to only contact emergency services if they were in "life-threatening" danger.

Brown said he would visit the worst-affected communities on Saturday to assess the damage and disruption as the clean-up begins.

"It’ll be a major, major job," he said.