Two thousand residents were evacuated from Edgecumbe in North Island after the Rangitaiki river inundated several houses close to the shore, Efe news reported.
A state of emergency was declared in neighbouring Whakatane, where another 2,000 people were evacuated.
According to official forecast, the water level of the Rangitaiki river will only begin to subside on Friday.
The police are patrolling these areas in boats to prevent the looting of abandoned houses, the New Zealand Herald reported, and added that all highways leading to these cities have been blocked.
Over a hundred schools remained closed on Thursday, the Education Ministry said.
Debbie became a category 4 storm while passing through Australia, where it displaced 90,000 people.
The storm was also declared a "catastrophe" due to its economic impact on the tourist and agricultural sectors in New South Wales.
Debbie is the most powerful cyclone to hit Australia since Yasi, which in 2011 caused giant waves and extensive damage in low-lying areas.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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Doraiah Chowdary Vundavally is a Software engineer at VTech . He is the news editor of SocialNews.XYZ and Freelance writer-contributes Telugu and English Columns on Films, Politics, and Gossips. He is the primary contributor for South Cinema Section of SocialNews.XYZ. His mission is to help to develop SocialNews.XYZ into a News website that has no bias or judgement towards any.