Domestic media reported a few flights had resumed operating by Monday afternoon from the airport in Wellington, the capital, although cancellations were still widespread after airport authorities said most morning flights were disrupted.
Air New Zealand said it hoped to resume services when conditions ease later on Monday, after it paused operations at Wellington, Napier and Palmerston North airports.
Online images showed flooded semi-rural neighbourhoods, inundated homes, trees fallen on vehicles and collapsed sections of road after waters receded.
The weather had been "absolutely terrifying", Marilyn Bulford, who lives in the rural town of Bunnythorpe, about 160 km north of Wellington, told the New Zealand Herald newspaper.
"I've never seen huge trees blowing around this much," she added. "It's so bad. I haven't seen anything like it."
The Wellington region accounted for more than half the 852 emergency calls received overnight, said Ken Cooper, assistant national commander of the emergency services.
"We had a very busy night, and our firefighters are continuing to respond to calls," he added.
More than 30,000 properties were without power, including about 10,000 customers in Wellington, said authorities, who have urged motorists to stay off roads, while several schools were closed as emergency crews tackled widespread damage.
The storm is forecast to bring heavy rains as it heads for the east coast of the South Island on Tuesday, the weather bureau said, with authorities warning of further disruption.
Raw sewage discharged after this month's failure of Wellington's main wastewater treatment plant in a storm was washed back onto the south coast by the weekend storm, in an incident some residents called a "poonami" on social media.
A 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 follows six deaths in January in a landslide triggered by heavy rains at Mount Maunganui on the North Island's east coast, bringing down soil and rubble on a site crowded with families on summer holidays.
