The men were brought aboard the 130,000-ton ship, where they were given medical attention, along with food and water, she said.
"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.
"We have notified theU.S. Coast Guardof this rescue and are working with the proper authorities to coordinate the debarkation of the group."
The rescue by the Disney Fantasy follows recent claims that a ship operated by Princess Cruise Lines failed to stop for three Panamanian fishermen adrift at sea, despite passengers alerting crew to their plight.
The sole survivor aboard the fishing boat, 18-year-old Adrian Vasquez, filed a lawsuit earlier this month against the company, arguing that its ship, the Star Princess, should have stopped and saved him.
The fishing boat, Fifty Cents, had been adrift for 15 days when it crossed paths with the Star Princess on March 10, according to the lawsuit. At the time, all three fishermen aboard were alive.
Vasquez was finally rescued by the Ecuadorian navy after 28 days adrift but his companions had died.
His lawsuit seeks compensation for physical, emotional and psychological injuries that it alleges he suffered as a result of the conduct of cruise line employees.
Princess Cruises said it deeply regrets the loss of life and was investigating the incident. It said it understands its responsibility under the law to aid a vessel in distress and noted its ships had carried out more than 30 rescues in the past.