In a statement, the Coast Guard said Tien Phuoc Nguyen jumped off the Royal Caribbean ship Adventure of the Seas Saturday night when it was about 15 miles east of Mona Island, CNN reported Monday.
Nguyen was on the cruise with his family, the Coast Guard said.
The ship immediately turned around to search for the passenger, Royal Caribbean International said in a statement.
A Coast Guard helicopter and a cutter joined the search Saturday night. The search continued Monday.
The cruise ship left the search area Sunday morning and resumed sailing to San Juan, from where it had departed about a week ago.
Royal Caribbean spokeswoman Cynthia Martinez said a passenger notified the captain another passenger was seen jumping overboard about 8:46 p.m. Saturday, ABC News reported.
Martinez said the ship's closed-circuit camera captured footage of Nguyen going overboard.
Coast Guard spokesman Ricardo Castrodad said it was possible Nguyen was still alive, although the weather in the Mona Passage was unpredictable.
"Weather conditions there typically change rapidly," he said. "It could be a good weather day and a weather system comes in and everything turns and becomes pretty nasty."
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