The tremor struck 40 kilometres (25 miles) west of Panguna on Papua New Guinea's Bougainville Island at a depth of 153 kilometres at 3:30pm local time (0430 GMT), the US Geological Survey said.
The Pacific Tsunami Warning Center initially warned that waves of between 0.3 and one metre (1-3 feet) above tide level were possible for some coastal areas of Papua New Guinea and the neighbouring Solomon Islands.
Smaller waves were possible for other nearby countries, it added.
Quakes of such magnitude are common in Papua New Guinea, which sits on the so-called Pacific "Ring of Fire", a hotspot for seismic activity due to friction between tectonic plates.
"Even though it is quite deep at 150 kilometres, because it is such a large earthquake, it will produce shaking on the surface," Geoscience Australia seismologist Spiro Spiliopoulos told AFP.
Australia and New Zealand both said they had assessed the threat and there was no danger to their coastlines.
A 7.9-magnitude quake struck off Papua New Guinea in mid-December as well, but no casualties were reported and an initial tsunami threat was later deemed to have passed.
In 2013 the Solomon Islands were hit by a devastating tsunami after an 8.0-magnitude earthquake rattled the region. That tsunami left at least 10 people dead, destroyed hundreds of homes and left thousands of people homeless.
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