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The earthquake prompted tsunami warnings and watches from several island chains to Australia and later New Zealand, but many of those were later canceled.

The low-lying Solomon Islands, however, were not spared. George Herming, a government spokesman, said the tsunami sent two nearly five-foot waves into the western side of Santa Cruz Island, damaging at least 50 homes.

The police commissioner of the islands, John Lansley, said his patrols reported that at least four people and perhaps more were likely killed by the waves and ensuing flooding.

Richard Dapo, a school principal on an island near Santa Cruz, told the Associated Press that he had been getting calls from families on the coast whose homes had been damaged by the waves. 

"I try to tell the people living on the coastline, 'Move inland, find a higher place. Make sure to keep away from the sea. Watch out for waves,'" he said.

The earthquake struck around 11 a.m. local time in the Santa Cruz Islands. There were conflicting reports as to the depth of the quake.

The Pacific Tsunami Warning Center said the tsunami warning was limited to the Solomon Islands, Vanuatu, Nauru, Papua New Guinea, Tuvalu, New Caledonia, Kosrae, Fiji, Kiribati, and Wallis and Futuna.

A lesser alert, a tsunami watch, was declared for American Samoa, Australia, Guam, the Northern Marianas, New Zealand and eastern Indonesia.

The earthquake was not only powerful but also shallow, which gave it significant potential to cause damage, said Barry Hirshorn, a geophysicist with the National Weather Service in Hawaii. Moreover, it was a thrust earthquake, he said, meaning that the sea floor moved up or down, not sideways, contributing to the potential for a dangerous tsunami.

But after the earthquake, as scientists watched to see how far a tsunami might spread, there were few early indications of a major threat beyond the immediate area, Mr. Hirshorn said. A water rise of about three feet had been observed close to the quake, he said, still high enough to be potentially damaging but probably not big enough to threaten distant shores.

In New Zealand, thousands of people were at the beach, swimming in the sea on a glorious summer afternoon on Waitangi Day, a national holiday — quite oblivious to the potential for a tsunami. Tsunami sirens were set off late in the afternoon there, and people in coastal areas were being told to stay off beaches and out of the sea, rivers and estuaries.

The New Zealand Herald reported Wednesday afternoon on its Web site that tsunami sirens in Suva, the capital of Fiji, had been warning people to stay inside or go to higher ground.

The Sydney Morning Herald reported on its Web site on Wednesday that the Solomon Islands' National Disaster Management Office had advised those living in low-lying areas, especially on Makira and Malaita, to move to higher ground.