PTWC said waves could be as high as 3 metres above the tide level in New Caledonia and Vanuatu.
New Zealand's Ministry of Civil Defence and Emergency Management, however, tweeted that there was no tsunami threat to the nation's coasts even though the tsunami alert issued for coasts within 1,000 km. The evacuation order from the regional police said western islands didn't need to evacuate but should remain vigilant.
New Caledonia, a collection of islands in the South Pacific, has been owned by the French since 1853.
Civil defence officials in Noumea said tsunami waves hit parts of the Loyalty Islands and the Isle of Pines, but caused no damage.
The warning also stated that tsunami waves of 1-3 feet (0.3-1 meters) were possible along some coasts of Fiji, according to PTWC.
A view of the bay of Noumea, the capital of New Caledonia, seen earlier this year.
Following the quake, there were two more aftershocks - one measuring 5.9 on the Richter scale 142km from New Caledonia, one at 5.7 magnitude and 131km away from New Caledonia.
There were no immediate reports of damage from the quake, but the Pacific Tsunami Warning Center said that waves had been "observed" and could reach up to three meters high.
"Based on that, we can say that this natural disaster has generated a tsunami, but we don't know the impact and how far it could go onshore", seismologist Spiro Spiliopoulos told AFP.
The Pacific Tsunami Warning Centre said there was no immediate risk of tsunami.
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