The fire that began at 2:50 a.m. Monday was extinguished about two hours later with no injuries reported. A cause wasn't immediately known.
Royal Caribbean said in a series of tweets that executives have met with passengers and that the cruise line is arranging flights for all 2,224 guests on Tuesday. It said passengers will receive a full refund of their fare and a certificate for a future cruise.
Aboard ship, the captain announced that passengers needed to go to their muster stations, rousing Mark J. Ormesher from his stateroom on the Grandeur of the Seas.
Ormesher said in an email to The Associated Press that immediately after the captain's announcement, his room attendant knocked on the door and told him and his girlfriend to grab their flotation devices, saying it wasn't a drill.
Orsmesher, a native of England, who lives in Manassas, Va., said he and his girlfriend smelled acrid smoke as they went to their muster station, the ship's casino. The crew quickly provided instruction.
"This encouraged calm amongst the passengers," he said. Passengers were required to remain at their stations for four hours, he said, and the captain "provided us as much information as we needed to stay safe."
Ormesher, who is 25 and on his first cruise, said the air conditioner had been shut off, and as the hours passed and the ship got hot, bottled water was passed around. The crew and passengers remained calm, and helped those who needed it. Crying babies were given formula and held while their parents used the bathrooms.
Royal Caribbean said in a statement on its website that most public areas and staterooms were safe and power, propulsion and communications systems worked without interruption. Photos show a substantial area on one end of the ship burned on several decks.
The ship had sailed from Baltimore on Friday and arrived in Freeport, Bahamas, Monday afternoon. It had been planned to be a seven-night cruise.
In Freeport, passenger Andrea Sanders of Washington, D.C., said she slept on the deck with hundreds of other passengers as smoke billowed out of the stern of the ship. "I was terrified with it being my first cruise," Sanders told The Freeport News as she ate lunch in port.
Royal Caribbean said all guests and 796 crew were safe and accounted for.
The company in a statement on its website said it is "deeply sorry for this unexpected development in our guests' vacation. We understand that this may have been a very stressful time for them. We appreciate their patience and cooperation in dealing with this unfortunate situation."
Carnival Corp. also had trouble with fire aboard ship earlier this year.
The 900-foot Triumph was disabled during a February cruise by an engine room fire in the Gulf of Mexico, leaving thousands of passengers to endure cold food, unsanitary conditions and power outages while the ship was towed to Mobile, Ala. It remained there for repairs until early May when it headed back to sea under its own power .
On the Grandeur, after passengers were allowed to leave their stations, Ormesher said he saw water on the outside of deck 5 and in the hallways. The mooring lines were destroyed he said; crew members brought new lines from storage.
The damage at the rear of the ship "looks bad," Ormesher said; burned out equipment was visible.
Magnus Alnebeck, general manager of the Pelican Bay Hotel, said his staff was asked to hold rooms for passengers, although it was not yet clear how many would stay there.
The ship will stay docked in Freeport at least overnight. The National Transportation Safety Board said in a tweet that it will join the U.S. Coast Guard in investigating the fire.