Strong rain caused several landslides, closing the road on Wednesday on Takaka Hill in the Tasman district in the north of the South Island and cutting about 6,000 locals and holidaymakers off from the rest of the country.
The worst of the storm has moved off to the east, but there are still warnings out for Wednesday evening (local time).
"In the spirit of South-South cooperation, which emphasises partner government ownership, following the assessment of the damages caused and priorities needing support, the Government of Tonga will identify the rehabilitation projects to be supported through the India-UN Development Partnership Fund", United Nations Office for South-South Cooperation said in a statement.
Civil Defence has advised residents not to panic buy supplies, and to only buy fuel for the coming week to ensure there is enough for everyone.
"India stands in solidarity with the friendly people of the Kingdom of Tonga in this hard hour of adversity", Modi said in his message offering the $1 million aid, according to a High Commission press release on Twitter.More news: Egypt opens Rafah crossing 'exceptionally' in both directions
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"They're holding up fine, they're quite resilient and self-sufficient", he said.
"We are expecting homes to be flooded".
The New Zealand military is now assisting in areas where the storm has made the most significant impact. Air New Zealand said all flights to the capital would be grounded from 2.45pm as weather authorities issued warnings of severe weather and heavy rain and gusts of up to 150 kph (93 mph). The city of Christchurch asked residents to keep showers short and delay washing clothes as the city's wastewater system came under pressure from rain water.
The owner of a supermarketin the township of Takaka in Golden Bay told Radio New Zealand that people were queuing outside his store well before itopened.
"The weather is really nice now", Kempthorne said. Earlier, the storm had caused extensive damage in Samoa and American Samoa.