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Dr Enrique Arango Arias, head of Cuba's National Seismological Service, told state media that there had been no serious damage or injuries reported on the island.
The Cayman Islands were rocked by several of the strong aftershocks that followed in the area, including one measured at magnitude 6.1. Water was cut off to much of Grand Cayman Island, and public schools were canceled for Wednesday.
The Pacific Tsunami Warning Center initially warned that the quake could generate waves 1 to 3 feet above normal in Cuba, Jamaica, the Cayman Islands, Honduras, Mexico and Belize, but issued a later message saying the danger had passed.
The quake was felt strongly in Santiago, the largest city in eastern Cuba, said Belkis Guerrero, who works in a Roman Catholic cultural center in the center of Santiago
"We were all sitting and we felt the chairs move," she said. "We heard the noise of everything moving around."
She said there was no apparent damage in the heart of the colonial city.
"It felt very strong but it doesn't look like anything happened," she told The Associated Press.
It was also felt a little farther east at the US Navy base at Guantanamo Bay, Cuba, on the southeastern coast of the island. There were no immediate reports of injuries or damages, said J. Overton, a spokesman for the installation, which has a total population of about 6,000 people.
Several South Florida buildings were evacuated as a precaution, according to city of Miami and Miami-Dade County officials. No injuries or road closures were reported. No shaking was felt at the Hard Rock stadium in Miami Gardens, which will host the Super Bowl on Sunday.
In the Cayman Islands, the quake left cracked roads and what appeared to be sewage spilling from cracked mains. There were no reports of injuries or more severe damage, said Kevin Morales, editor-in-chief of the Cayman Compass newspaper.
The islands experience so few earthquakes that newsroom staff were puzzled when it hit, he said.
"It was just like a big dump truck was rolling past," Morales said. "Then it continued and got more intense."
Dr. Stenette Davis, a psychiatrist at a Cayman Islands hospital, said he saw manhole covers blown off by the force of the quake, and sewage exploding into the street, but no more serious damage.
Claude Diedrick, 71, who owns a fencing business in Montego Bay, said he was sitting in his vehicle reading when the earth began to sway.
"It felt to me like I was on a bridge and like there were two or three heavy trucks and the bridge was rocking but there were no trucks," he said.
He said he had seen no damage around his home in northern Jamaica.
Mexico's National Seismological Service reported that the quake was felt in five states including as far away as Veracruz, on the country's Gulf Coast.
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