Authorities canceled warnings for tsunamis on more distant coasts.
Solomons officials reported two 1.5-meter (4 foot, 11-inch) waves hit the western side of Santa Cruz Island, damaging between 70 and 80 homes and properties, said George Herming, a spokesman for the prime minister. Many villagers had headed to higher ground as a precaution, Herming said.
Solomon Islands Police Commissioner John Lansley said local police patrols had reported that several people were presumed dead, though the reports were still being verified.
"Sadly, we believe some people have lost their lives," he said. "At the moment we potentially know of four, but there may of course be more."
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