But authorities warned waves of up to three metres (11 feet) were possible in New Caledonia and Vanuatu, where residents in the capital Port Vila received SMS messages ordering them to "move to higher grounds".
They knew to head into the highlands when they felt a long or strong quake, she said.
New Zealand Prime Minister Jacinda Ardern posted on Instagram: "Hope everyone is ok out there".
This latest tsunami threat comes not long after another powerful quake in the early morning hours.
No damage or injuries were reported from the earlier quakes, both of which generated tsunami warnings that were later lifted.
"We expect New Zealand coastal areas to experience strong and unusual currents and unpredictable surges at the shore", the National Emergency Management Agency (NEMA) said in a tsunami advisory after the quake off the Kermadec Islands.
An emergency alert was issued for all coastal areas around Auckland, a city of 1.7 million, where people were told to stay away from the water's edge.
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Their coasts could see wave surges as high as 3m (10ft), while parts of South America - including Peru, Ecuador and Chile - were warned they could see 1m waves reaching their coasts.
The third and strongest quake struck the Kermadec Islands, a mostly uninhabitated group of islands some 800 km (500 miles) northeast of the North Island, on Friday morning, shortly after a 7.4 magnitude natural disaster in the same region.
Those North Island residents who have had to "pick up their homes and evacuate" had done exceptionally well, said Allan.
It was an 8.1 magnitude natural disaster whose epicenter lay in the ocean, about 600 miles north of New Zealand.
"This is about as big as it gets", she said.
Prior to the the magnitude 8.1 quake, there was a magnitude 7.4 quake in the same region at 9:41 a.m. "I can only thank and acknowledge the tireless efforts of the men and women from up and down the coast who knew how to act, when to act, and what to do".
The closest major city to the epicentre is Gisborne, with a population of about 35,500 residents.