A 6.5-magnitude earthquake has hit off the Solomon Islands, the latest powerful aftershock following a 8.0-magnitude quake that sparked a tsunami four days ago, US seismologists said.

The US Geological Survey said the quake struck this morning 29 kilometres south-southwest of Lata, the main town on remote Ndende island in the Santa Cruz Islands, which are part of the Solomons, at a depth of 18 kilometres.

It was the latest in a series of powerful aftershocks to hit the remote region since a deadly 8.0-magnitude earthquake on Wednesday triggered a tsunami, killing at least 13 people, destroying villages and leaving thousands homeless.

The tremor was not expected to generate a widespread tsunami, the Pacific Tsunami Warning Centre said.

Geoscience Australia also measured it at 6.5 but centred at a greater depth of 36 kilometres.

A further 12 houses were reported destroyed following a 6.8 magnitude tremor on Friday and another measuring 7.0, which sent villagers fleeing to higher ground in fear of another tsunami.

The Solomon Islands government has declared the outlying Santa Cruz Islands a disaster area as the aftershocks continue to hamper relief efforts.

Because of a fragile communications system, officials in the capital Honiara were struggling to get a clear picture of the extent of damage, but the Red Cross said food, water and shelter were a priority for quake-hit villages.