Another powerful quake struck near Kirakira this morning - a 6.7 magnitude quake at a depth of 33km.
The undersea quake hit 71km west of the city of Kirakira, which is on the country's biggest island, Makira.
National Disaster Management Office director Loti Yates said there was no tsunami threat from this morning's quake but he was expecting more reports of damage.
Mr Yates said multiple quakes of magnitude 5 and above have hampered relief operations still under way in the Makira area.
"There have been stories coming around that people are currently very unsettled, whether they will start building or they will start going back to their normal activities. But this ongoing shaking has been quite nerve-racking for them."
No tsunami warning has been issued by the Pacific Tsunami Warning Center in Hawaii following the quake.
The country has been hit by a string of earthquakes in the past month, including the 7.8 magnitude quake that killed one person.
Photo: USGS An earthquake of magnitude 6.7 has struck west of Solomon Islands at a depth of 33 kilometres.