The crew of the Fantasy spotted the raft Sunday afternoon, CNN reported. Rebecca Peddie of Disney Cruise Lines said they were brought aboard the Fantasy, examined by a doctor and fed.
The U.S. Coast Guard was notified of the rescue, Peddie said, and the company was working with "the proper authorities" on when and where the men should leave the ship.
"We are proud of our Disney Fantasy crew members, who skillfully demonstrated their training and commitment to maritime protocols around saving lives at sea," she said.
Adrian Vasquez, 18, a Panamanian fisherman, recently filed a lawsuit against Princess Cruise Lines, charging the Star Princess passed by a Panamanian fishing vessel, the Fifty Cents, which had been drifting for 15 days.
By the time the Ecuadorian Navy came to the vessel's aid, 13 days later, Vasquez's three companions had died.
Celebrity Families of 2014 [PHOTOS]