Tsunami waves up to 2 metres high struck parts of French Polynesia, and other Pacific nations were evacuating coastal areas.
Residents were being warned early Sunday morning that tsunamis can consist of several waves and they should remain vigilant.
Monique Richeton, mayor of Rikitea, French Polynesia, said the first wave struck Gambier early Sunday at less than one metre and no damage was reported.
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In Samoa, where 183 people died in a tsunami in September, police said most people were moved out of low-lying areas by 6 a.m. local (1800 GMT Saturday). The waves are expected there about 8 a.m. (2000 GMT Saturday).
“The evacuation is going pretty well, with most people in higher ground already,” on the main island of Upolu, police spokesman Tavita Moeono said.
In the Cook Islands, police sirens, text messages and local broadcasts alerted people during the late night and early morning to move inland to high ground and away from the coast.
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Police in the capital, Avarua, said coastal evacuations from villages and tourist resorts had gone smoothly, but they were concerned a high tide at the main island of Rarotonga could see any tsunami wave surge further inland.
New Zealand warned that “non-destructive” tsunami waves of less than three feet could hit the entire east coast of the country’s two main islands and its Chatham Islands territory, some 312 miles (500 kilometres) east of New Zealand.
The Ministry of Civil Defence and Emergency Management said models suggest waves of between three and 10 feet could hit parts of Chatham Islands and Banks Peninsula on South Island.
Residents of low-lying coastal areas on Banks Peninsula were told to prepare to evacuate their homes for up to 24 hours, the only such advisory issued for New Zealand.