Spokesman Ricardo Castrodad said Saturday that the search was suspended late Friday.
The man was identified as 42-year-old Jason Gregory Rappe of Olympia. His wife reported him missing Thursday from the Holland America cruise ship Eurodam. A baseball cap that belonged to him was found on one of the decks.
Rappe was reported missing as the ship traveled from St. Thomas in the U.S. Virgin Islands to the Bahamas.
The ship had turned around to help search for Rappe but later resumed its voyage. It is expected to arrive in Fort Lauderdale, Florida, on Saturday.