NIUE DAMAGE
However, some officials say damage caused by Cyclone Heta was not as widespread as previously believed.
At least 12 houses have been flattened, but hurricane-proof buildings are still standing, a New Zealand Foreign Ministry spokesman said.
Some 200 people are reported to be homeless.
A New Zealand air force plane flew in carrying Niue Premier Young Vivian, who was in New Zealand arranging his wife's funeral when the storm struck.
"Things don't look too good at the moment. I have cried for my country," he said.
'Devastation'
Niue government secretary Cecelia Talagi said a foreign volunteer worker and the baby of the woman killed have been seriously injured. They have been evacuated to Auckland.
"Yesterday morning we woke up to a scene of so much devastation, it was just unbelievable. Cyclone Heta was just so fast, furious and ruthless," she said.
The baby was found next to his mother's body amongst the rubble of their home in the capital Alofi.
Twenty New Zealanders who were on holiday on Niue have been accounted for.
Communicating with the island is difficult after its telecommunications satellite dish was destroyed along with the building in which it was stored.
More aid and emergency workers will be flown in on Friday to Niue, which lies about 2,700km (1,675 miles) north-east of New Zealand's capital, Wellington.
More Niueans live in New Zealand than in their own country, because of unemployment.
A tiny coral island, Niue would have had no protection against the force of Cyclone Heta, which had reached a strength of category five, the highest cyclone rating.
It had already hit American and Western Samoa, Tokelau and the northern islands of Tonga.
Samoa suffered damage to crops, roads and buildings, but reported no serious casualties.
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