As many as nine aftershocks have been recorded since the quake, the largest measuring 7.0 magnitude.
Waves of up 1m are possible in Fiji.
New Zealand authorities issued a similar tsunami warning after the quake, but that was quickly rescinded.
PTWC said waves could be as high as 3 metres above the tide level in New Caledonia and Vanuatu.
Based on current information, the initial assessment is that the natural disaster is unlikely to have caused a tsunami that will affect New Zealand.
A powerful 7.0-magnitude natural disaster struck off New Caledonia, according to monitors, hours after an initial 7.5-magnitude quake was recorded in the same area on Wednesday, prompting a tsunami alert and evacuations on the Pacific island.
"The good news is, we have had no injuries or damage", said Oliver Ciry, a spokesman for New Caledonia's directorate for civil protection and risk management, adding that abnormal movements of the sea off the east coast and around the Loyalty Islands had been spotted earlier.
The Pacific Tsunami Warning Center confirmed tsunami waves had been observed following the quake.
New Caledonia, a French overseas territory, has a population of about 259,000. PTWC said it did not pose a tsunami threat.
The French territory, comprising of dozens of islands, is around 1,500 miles north of New Zealand.
Civil Defence said there was no tsunami threat to New Zealand.
The Ring of Fire refers to a string of volcanoes, quake sites and tectonic plates around the Pacific.
Its citizens last month rejected independence in a referendum, though the vote revealed lower-then-expected support for remaining part of France.