New Zealand’s capital, Wellington, and the surrounding region were under a state of emergency on Tuesday, after heavy rains triggered flash flooding and landslides that swept away cars, forced more than 100 schools to close, and buried roads and homes.

Some areas recorded more than three inches of rain within an hour, the country’s weather agency, MetService, said. The emergency declaration, made by the authorities on Monday afternoon, gives them more power to respond and to order evacuations. Overnight, the authorities urged residents in low-lying areas to relocate until it was safe to return. The state of emergency was lifted in some areas on Tuesday.

There were no reports of fatalities, but one man is missing after the property he was living in was hit by floodwaters and debris, the police said. Greater Wellington, which covers about 3,100 square miles on the southern tip of North Island, has more than half a million residents.

The heaviest of the rainfall had concluded by Tuesday morning, but more wet weather was expected in the coming days, MetService said. “Sodden soils increase the risk for slips and local flooding remains an issue,” it warned.

Andrew Little, Wellington’s mayor, said it would take a while to clean up the city and urged people to stay indoors until the wet weather eased.

“Trees have come down, manhole covers have been lifted and there is debris in the streets,” he said in a Facebook video on Tuesday. “You must keep yourself safe.”

Images posted on social media showed roads and homes partially buried by landslides, a car perched on top of a fence, and muddy floodwaters rushing through homes and businesses.

On Tuesday, 120 schools were closed across the capital region, the education department said.

Dana McDonald, the lead teacher at the South Wellington Montessori School, said about three feet of water had washed through the preschool, which can cater to as many as 29 students, and “destroyed everything.”

“We’d just set up for term two, which was meant to start yesterday, and the classroom was really ready for the children, and now we’ve got absolutely nothing,” she said.

Ms. McDonald said work was underway to repair the school, with the walls and carpets already removed, while they searched for a temporary campus.

The weather agency said the rain would track further north in the coming days before gradually easing.