The magnitude 7.2 and 6.5 quakes struck close together around 2148 GMT and occurred around 55 miles (88 km) south-southeast of the small South Pacific island of Gizo, the U.S. Geological Survey and Pacific Tsunami Warning Centres said.
"The reports say villages and houses have been damaged by landslides rather than tsunamis, but we do not have any confirmation of deaths or injuries," a spokesman for the National Disaster Management Office told Reuters from Honiara.
The quakes occurred at depths of between 33 km (20.5 miles) and 36 km and Gizo police earlier said possible tsunami waves struck uninhabited Tetepare island, home to a nature reserve.
Landslides were tiggered on Tetepare and nearby Rendova island, in Western Province, which was a World War Two Patrol Boat base used by former U.S. President John F. Kennedy, disaster office spokesman Brian Tom said.
Rendova had a population of 3,679 at last census in 1999 and covers 400 sq km (160 sq. miles).
The Pacific warning centre said there was no wider tsunami threat to regional coastlines.
A large 8.1 magnitude quake and subsequent tsunami struck Gizo in 2007, killing 52 people and leaving thousands homeless. The Solomons are part of the Pacific "Ring of Fire," where colliding continental plates frequently causes seismic activity.
A series of tsunamis swept into the island nations of Tonga, Samoa and American Samoa in September last year, killing more than 100 people and levelling several villages.
(Reporting by Rob Taylor; Editing by Ron Popeski)
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