A 7.3-magnitude earthquake struck at 2.27am (12.27am AEDT) at a depth of 10 kilometres under the ocean, about 178 kilometres north-east of the city of Gisborne and near the Kermadec Islands.
Another 7.4-magnitude quake hit at 6.40am local time and a third – the largest at 8.1-magnitude – struck at 8.28am.
There have been no reports of any fatalities or injuries, and no buildings appear to have been damaged by the earthquake.
People living in New Zealand’s Bay of Islands to Whangarei, Matata to Tolga Bay and Great Barrier Island have been told to evacuate immediately and move as far as inland as possible.
Video footage has shown long lines of cars, with locals standing and waiting at higher ground.
A tsunami warning is also current for Australia’s Norfolk Island.
The warning has not yet been extended to the Australian mainland however the Bureau of Meteorology has issued a watch alert in case conditions develop.
Authorities believe it could possibly impact Norfolk Island around 10am local time.
“People are strongly advised by Norfolk Island police in all threatened areas to get out of the water and move away from the immediate water’s edge of beaches, marinas, harbours, coastal estuaries and rock platforms,” the Joint Australian Tsunami Warning Centre said.
“Boats in harbours, estuaries or shallow coastal water should return to shore.
“Secure your boat and move away from the waterfront.
“Vessels already at sea should stay offshore in water at least 25 metres deep until further advised.
“Do not go to the coast to watch the tsunami.
“Check that your neighbours have received this advice.”
Long-time Gisborne resident Karen Clune said the first quake made her feel physically ill and she hadn’t been able to sleep thanks to as many as 20 aftershocks.
“It was awful. The house was shaking and a few of my things on the shelves fell off,” she told 9news.com.au.
“It was similar to the one in 2009 that did a lot of damage.”
Even though the quake struck in the middle of the night, people took to social media to report feeling it almost from one end of the North Island to the other.
“I’m quite frightened, I’ve got no idea if there’s going to be a tsunami. It was massive.
“It’s the biggest I’ve felt in a long, long time and I’m 80.”
Wairarapa MP Kieran McAnulty felt the quake as far south as Masterton, near the bottom of the North Island.
The US Tsunami Warning System had predicted waves of 30cm to one metre.
Residents of Gisborne reported light to moderate shaking, the US Geological Survey said.
A magnitude 6.3 quake hit the city of Christchurch in 2011, killing 185 people and destroying much of its downtown.