The quake was detected at 0257 GMT around 340 kilometres (210 miles) east of Vao city in New Caledonia, a French Pacific territory, according to the US Geological Survey (USGS).
In New Caledonia, the police had evacuated the coast and tsunami sirens had been activated.
"The first waves arrived at Mare and Ile des Pins (in New Caledonia) but they were no higher than 50 centimetres" above the usual tide, according to civil security chief Frederic Marchi-Leccia.
"Sirens rang all around the territory, and the security forces and firefighters evacuated the coastal areas."
Waves of around half a metre above tide level were observed at Lenakel in Vanuatu, with slightly smaller ones observed or predicted for several other Pacific islands, according to the Honolulu-based Pacific Tsunami Warning Center.
Vanuatu authorities called on residents to evacuate coastal areas lower than 12 metres above sea level and less than 300 metres from the shoreline on Friday.
Anna Erick, who runs a beachfront hotel on Tanna island in Vanuatu, told AFP she decided to head to higher ground with her children after unusually big waves began to crash on a nearby beach.
She said the waves were about knee-high and although she had decided to evacuate out of precaution, others were still watching the waves.
Benie Simo, a local tour operator on Mystery Island in Vanuatu, said he had received a government warning via text message to evacuate and had also moved to higher ground.
The waves, he said, were coming up "really high, but it's not much". Simo described the waves as being about one to two metres high, adding that so far there were no reports of damage.
"People are just doing exactly what they're being told... So they're just going up to the higher ground until they're told it's all safe to come back down," he said.
"Gotta be cautious, and people just follow the protocols."
- 'Ring of Fire' -
Waves were forecast to be no higher than 0.3 metres above the tide level for all other Pacific territories, the tsunami centre said in an update.
A hotel receptionist in the New Caledonia capital Noumea told AFP she had felt no shaking from the tremor.
Others in the city, however, reported feeling strong shaking.
"We were on the 14th floor. We were on the sofa quietly watching TV, we were finishing lunch, and then it shook for a few seconds. It was super scary," one resident told a local radio programme.
Another, named Anne-Laure, told the programme: "We didn't think... we went to get my sister-in-law and immediately we came to higher ground."
Meanwhile, a travel agent on Ile des Pins on the eastern edge of the New Caledonia archipelago said she had also not felt the tremor or heard any evacuation warning.
"Everybody is still on the beach and in the restaurants," she said.
The Australian bureau of meteorology said there was "no land threat to the Australian mainland or Australian territories".
Earthquakes are common along the Pacific "Ring of Fire", an arc of intense seismic activity that stretches through Southeast Asia and across the Pacific basin.
Earlier this month, an earthquake in Japan killed one person, injured dozens more and destroyed several buildings.
And in April, an evacuation order was issued to coastal dwellers on a remote Philippine island after a 6.2-magnitude quake struck in the ocean off the archipelago, triggering a tsunami warning, though there were no reports of damage.
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