New Zealand said it may need billions of dollars to recover from Cyclone Gabrielle as the country extended the national state of emergency by another week.

Prime Minister Chris Hipkins confirmed 11 people have so far died in the wake of the devastating flash flooding and high winds which lashed the North Island last week.

"Our thoughts remain with families and communities grieving loved ones during such a difficult time," he added.

Hipkins has warned the final death toll could rise, but the number of people who police were still looking to contact had fallen to about 2,300.

The full extent of the cyclone's destruction is becoming clearer, as highways, power and telecommunications are re-established.

The raging torrent of floodwater the cyclone unleashed swept away or badly damaged homes, businesses, bridges and roads across New Zealand.

Finance Minister Grant Robertson on Monday pledged $300 million New Zealand dollars ($187 million) of relief.

Robertson warned the money pledged so far will only "scratch the surface" of the final figure needed, which he predicts will cost taxpayers "billions of dollars."

"We have a long job ahead of us to rebuild after this disaster," warned Robertson who Hipkins has also made cyclone recovery minister, "but we have the resources and the will to do it."

According to Hipkins, 15,000 North Island households remain without power, mostly in the east coast cities of Gisborne and Napier, where floodwaters poured into many homes.

After spending the weekend visiting hard-hit communities, Hipkins said the national state of emergency declared last week has been extended by another seven days.

"While some areas are starting to work on recovery, others are still very much in the emergency response phase," he added.

This is only the third time in New Zealand's 183-year history that a national state of emergency has been declared.

The other two were the 2019 Christchurch attacks and the COVID-19 pandemic.