The Solomon Times Online reported at least seven people have so far been confirmed dead in the Solomons' Santa Cruz Islands struck by the offshore quake and a trailing 3-foot tall tsunami early Wednesday.
TV New Zealand reported eight people had been confirmed dead.
The television channel quoted World Vision relief group as saying about 3,500 people were affected by the disaster and at least 700 homes had been damaged. The region also has been plagued by numerous aftershocks.
"Many of the homes, sadly, have been swept away and a couple of villages have been completely swept away and that's why we need to get people out there as soon as we can," Solomon Islands Police Commissioner John Lansley in the capital Honiara told the television channel.
He said the islands' airport runway was being cleared of debris dumped by the tsunami, and until then boats would ferry emergency crews and medical and other supplies to the stricken areas.
"The injury toll is not that clear, we know there are still a number of people missing and we are still trying to assess the situation on the ground," he said. It was feared many of the missing people might have been swept into the Pacific Ocean.
The Solomon Times said the worst-hit areas included the villages of Mbimbe, Nea, Bania, Manoputi, and Nela.
Authorities told the newspaper assessment of the full extent of the damage can be made only after high water levels recede from some of the inaccessible areas, which could push the death toll higher.
Solomon Islands Prime Minister Gordon Darcy Lilo, expressing condolence to the families of the dead, assured everything was being done to ensure emergency supplies reach affected people as soon as possible
The 8-magnitude earthquake, as measured by the U.S. Geological Survey, struck west-southwest of the Santa Cruz Islands.
A doctor with a charity group told TVNZ considerable debris also has been reported in water supplies and the cleanup effort also would require removing dead animals.
The quake was first believed to be a shallow one, but the USGS said it was at a depth of nearly 18 miles.
The tsunami warning, before it was lifted by the Pacific Tsunami Warning Center in Hawaii, covered a wide region including the Solomon Islands, Vanuatu, Nauru, Papua New Guinea, Tuvalu, New Caledonia, Kosrae, Fiji, Kiribati, Wallis and Futuna. The center also had posted a tsunami watch for other areas in the region, including New Zealand, Australia, Indonesia, the Marshall Islands, American Samoa and Guam.
In Fiji, TVNZ reported residents responded quickly by heading out of the capital Suva. Schools were closed and hospitals and hotels in the low-lying areas were speedily evacuated.
In 2007, a tsunami following an 8-magnitude earthquake killed at least 52 people on the Solomons and left thousands homeless.