Most flights in and out of the capital Wellington were cancelled or delayed on Monday morning, the airport said. Air New Zealand paused operations at Wellington, Napier and Palmerston North airports, media reported.
More than 30,000 properties were without power, including about 10,000 customers in Wellington, authorities said.
Motorists across the Wellington region have been urged to stay off the roads, while several schools were closed as emergency crews responded to widespread damage.
"We had a very busy night, and our firefighters are continuing to respond to calls," Emergency New Zealand Assistant National Commander Ken Cooper said.
More than half the 852 emergency calls received overnight came from the Wellington region, he added.
Wellington's main wastewater treatment plant failed in a storm earlier in February, forcing the discharge of raw sewage off the south coast.
The weekend storm has washed and blown the pollution back onto the coast in what some residents are calling a "poonami" on social media.
Images shared online showed flooded semi-rural neighbourhoods, inundated homes and collapsed sections of road after the waters receded.
Marilyn Bulford, a resident of the rural town of Bunnythorpe, about 160 kilometres north of Wellington, told the New Zealand Herald the weather had been "absolutely terrifying".
"It's so bad. I haven't seen anything like it," she said.
"There are trees down everywhere ... on cars, on fences, on the road ... the golf course, that's a complete mess. I've never seen huge trees blowing around this much," she said.
A deepening low-pressure system east of the North Island has battered several regions since the weekend, bringing heavy rain and severe gales. A man was found dead on Saturday in a submerged vehicle on a highway.
The storm is forecast to move toward the South Island on Tuesday, with authorities warning of further disruption.
