The aftershock comes after an natural disaster struck 168.2 km (104.5 miles) from the small town of Tadine on the Loyalty Islands, New Caledonia.
The PTWC said hazardous waves below 30cm were possible right across the Pacific, including in Australia, China, Columbia, Hawaii, Indonesia, Japan, Malaysia, Mexico, PNG and New Zealand.
The tsunami waves were observed at Maré Island in New Caledonia and Lenakel in Vanuatu.
Mr Rene said so far there were no reports of a tsunami or damage in the Loyalty islands.
"I was in a meeting at the town hall and we felt a small tremor then a bigger one", he told AFP. "For now, nothing serious has happened".
Judith Rostain, a freelance journalist based in New Caledonia's capital Noumea, said there was no damage to the city and that the threat of a tsunami appeared to have passed.
Waves measured by quake monitors around the region only reached about 72cm on the island of Tanna, Vanuatu.
"We get a lot of earthquakes every year", he said.
A spokeswoman for the Directorate of Civil Protection and Risk Management said: "We have set off the alarm on the exterior of New Caledonia but we don't have any immediate assessment of potential damage".
CCTV footage showed bathers still frolicking in crystalline seas off Noumea, seemingly unaware of the seriousness of the threat on the other coast, just 50 kilometres away.
Earthquakes are generally more destructive when the epicentre is near the surface.
Last month, voters in New Caledonia elected to remain a territory of France rather than becoming independent.