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The quake struck 62km northwest of San Antonio at 11:23 pm local time (03:20 GMT) at a depth of 10km, the agency said.
San Antonio is home to Rafael Hernandez Airport, a key air link to the mainland US.
In 2010 nearby Haiti was struck by a devastating 7.0 magnitude earthquake that killed more than 250,000 people and crippled the nation's infrastructure.
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