The U.S. Geological Survey said the quake occurred about 100 miles (160 km) southeast of the small island of Gizo.
The Pacific Tsunami Warning Center in Hawaii said the quake, at a depth of 33 km (20 miles), may cause a local tsunami, but that there was no Pacific-wide threat.
"We have had no reports of damage and no tsunami threat. It was quite a bit bigger than the previous night," a police officer in Gizo told Reuters by telephone.
Two strong earthquakes damaged villages and triggered landslides in remote parts of the Solomon Islands on Monday, but there were no immediate reports of casualties.
The magnitude 7.2 and 6.5 quakes struck close together about 55 miles (88 km) south-southeast of Gizo, the U.S. Geological Survey said.
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" on which colliding continental plates frequently cause seismic activity.
A series of tsunamis swept into the island nations of Tonga, Samoa and American Samoa in September 2009, killing more than 100 people and levelling several villages. (Reporting by Michael Perry; Editing by Nick Macfie)
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