The large quake, which was originally believed to measure 6.3 magnitude, struck southeast of the islands, the US Geological Survey reports.
The shallow quake was only 5.8km deep and the epicentre was 347km east of Kira Kira in the Solomon Islands.
A tsunami warning has been issued for the south Pacific islands, by the Pacific Tsunami Warning Center in Hawaii.
The Solomon Islands National Disaster Management office has issued Tsunami Warning for Temotu Province, Malaita Province, Makira Province, Central Province and Guadalcanal Province.
People are currently advised to move to higher grounds as a precaution. The damages in Temotu are currenlty being assessed by the Disaster Office.
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