* Three offshore quakes of magnitude 7.2-8.1 strike over 8 hours
* Small tsunami waves hit New Zealand's North Island
* Authorities cancel tsunami warnings after biggest waves pass (Adds Ardern comment, updated tsunami advice)
By Praveen Menon
WELLINGTON, March 5 (Reuters) - A powerful series of undersea quakes struck north-east of New Zealand on Friday, but tsunami waves that forced many people on the country's North Island to flee to high ground passed without causing substantial damage.
Officials had warned that waves could reach three metres (10 feet) above high tide levels after the quakes - the strongest a magnitude 8.1 - but the threat had passed by the afternoon, the National Emergency Management Agency (NEMA) said.
"It's hard not to feel like our country is having a run of bad luck, when you have an earthquake, tsunami and pandemic to contend with all in one day," New Zealand Prime Minister Jacinda Ardern said.
Video footage posted on social media showed surges of water entering a marina in Northland and on the North Island's East Cape region.
Earlier on Friday, workers, students and residents in areas like Northland and Bay of Plenty, on the northern coast near Auckland, fled beachside towns for higher ground after the three quakes, striking in an eight-hour period, triggered blaring tsunami sirens and warnings to evacuate via text messages.
An emergency alert was issued for coastal areas around the South Pacific country of 5 million, with people to stay away from the water's edge. There were no reports of damage or casualties from the quakes.
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 earthquake in the same region. Earlier, a large 7.2 magnitude earthquake struck just east of the North Island.
Linda Tatare, a resident of Anaura Bay, on the North Island's east coast, said the small community of about 50 left for higher ground in the morning.
"Everyone, and their dogs, are up in the hills," Tatare told Reuters.
"We are safe. We can all see our properties from here."
Tsunami warnings were also put out for Pacific islands including New Caledonia and Vanuatu, while smaller tsunami waves may be recorded as far away as Antarctica and parts of South America, the U.S. Pacific Tsunami Warning Center said.
Friday's series of quakes was caused by tectonic movement on the boundary of the Australian and Pacific plates, part of the so-called Pacific Ring of Fire that New Zealand sits on.
A decade ago, a magnitude 6.3 quake killed 185 people in the South Island city of Christchurch. issued a marine tsunami threat for Norfolk Island, a tiny Australian territory with about 1,750 residents, but said there was no threat to the mainland.
Norfolk Island residents in areas threatened by land inundation or flooding were advised to go to higher ground or inland, the Bureau of Meteorology said, as small tsunami waves impacted the coastline.