Josh and Sharyn Hakken allegedly kidnapped their sons, Chase, 2, and Cole, 4, from their grandmother's Tampa, Fla., home last Wednesday, leaving the woman tied up.
The U.S. Interests Section in Havana told CNN Cuban authorities were cooperating in the investigation.
CNN said the Hakkens' sailboat, the Salty, was spotted in the marina and a man matching Josh Hakken's description confirmed his identity but declined to answer questions.
Sheriff's officials in Tampa describe Hakken as an anti-government protester and say he may be armed.
The Hakkens lost custody of their children following an incident at a Slidell, La., hotel where police said they found the couple acting bizarrely. Weapons and narcotics were found at the scene, CNN said.
The U.S. Interests Section of the Swiss Embassy in Havana represents American interests in Cuba, since the United States does not have formal diplomatic relations with the Communist island nation.
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