Carnival has also brought meals aboard from two other cruise ships, the cruise line said Monday. Earlier, Carnival said in a statement that hot coffee was available, among other options.
"All our guests are safe, and we're doing everything we can to make them as comfortable as possible," Carnival CEO Gerry Cahill said Monday night. "We're terribly sorry for the inconvenience, discomfort and frustration our guests are feeling."
In addition to the two Carnival ships that have brought supplies, the U.S. Coast Guard cutter Vigorous is steaming nearby.
The Triumph is "in deep water and not near any hazards to navigation," said Cmdr. Greg Magee, commander of the Vigorous.
Carnival initially planned to tow the ship to Progreso, Mexico, but strong currents that pushed it 90 miles north by Monday night prompted the decision to move the ship to Mobile instead. The change will also make it easier on the 900 passengers who don't have passports, the cruise line said.
Passengers will get a free flight home, a full refund for their trip and most expenses aboard, and a credit for another cruise, Carnival said.
The incident has forced Carnival to cancel the ship's next two departures, refund bookings for those trips and offer those passengers discounts on future cruises.
In 2010, the Carnival's cruise ship Splendor lost power after an engine room fire, leaving it drifting off the Pacific coast of Mexico. The USS Ronald Reagan ferried 60,000 pounds of supplies for the ship's passengers and crew as the ship was towed to San Diego.