The tremor struck 40 kilometres west of Panguna on Papua New Guinea's Bougainville Island at a depth of 153 kilometres at 3:30pm local time (0430 GMT), the USGS said. It its preliminary assessment it added that light to moderate damage was possible on Bougainville Island.
The Pacific Tsunami Warning Center warned that waves of between 0.3 and one metre (1-3 feet) above tide level were possible for some coastal areas of PNG and the neighbouring Solomon Islands. Smaller waves were possible for other nearby countries, it added.
The warning was withdrawn after the tsunami threat passed on Sunday evening.
Earthquakes are common near Papua New Guinea. The Solomon Islands are located in the Pacific's geologically active "Ring of Fire."
A 7.9-magnitude quake struck off Papua New Guinea in mid-December, 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.