The US Marshals Service said three men rescued by a Disney Cruise Line vessel were arrested after it was discovered they were fugitives apparently trying to flee to Cuba.

The 2,500-berth Disney Fantasy (built 2012) encountered Luis Rivera-Garcia, Juliet Estrada-Perez and Enrique Gonzalez-Torres yesterday morning while they were clinging to a capsized boat 64 kilometres from Varadero, Cuba.

The men, Cuban nationals but residents in the US, were then turned over the US Coast Guard at sea, according to US Marshal Amos Rojas.

US Marshal Amos Rojas

Officials of that agency carried out a fingerprint analysis that determined that there were outstanding arrests warrants against two of the men.

Authorities eventually realised that all three were wanted for violating their supervised release on credit card fraud charges in New Orleans, so they were turned over deputy marshals in Key West, Florida.

"US Marshals believe the three co-defendants may have been fleeing to Cuba to avoid prosecution in the US," the agency said.

Rivera-Garcia, 26, Estrada-Perez, 23, and Gonzalez-Torres, 23, had been arrested in 2015 by the US Secret Service and released on bond, but they were not allowed to leave certain parts of Louisiana and Florida.

Estrada-Perez and Rivera-Garcia were arrested again on 18 April after being found to be in position of 28 stolen credit cards. They were charged with trafficking in stolen credit cards, according to the US Marshals Service.