The company warned it would take even longer to safely remove passengers from the Triumph when it reached the port in Mobile.
"Given that this is the [largest] ship brought to this port [and] it is being towed, the timetable provided is our best estimate," Carnival tweeted Thursday afternoon.
"The debark process will be challenging given the limited [number] of elevators [and] power," the company continued. "The disembarkation process could take as long as 4-5 [hours]."
Carnival has said there are 3,143 passengers aboard the cruise ship and 1,086 crew members. No injuries have been reported.
The company has promised passengers refunds of their ticket purchases and credits for future cruises.
The company has also said that it is positioning 200 employees in Mobile to receive passengers when the disabled cruise ship arrives in the Alabama port city, and is reserving hotels in the city for passengers who want to rest when they get off the boat.
The Triumph cruise was supposed to last four days after departing from Galveston, Texas, last Thursday. Carnival said the engine fire left the ship without enough power to continue its journey.
"The ship is currently without propulsion and is operating on emergency generator power while the ship's technical crew assesses the damage and attempts to restore power," the company said in a Facebook post this week.
At least one lawmaker, Rep. Doris Matsui (D-Calif.), has called for a congressional investigation into the disabled Carnival cruise liner.
Matsui sponsored legislation passed by Congress in 2011 to beef up safety requirements for passengers on cruise ships.
She said Thursday that the Triumph's debilitation showed the need for more federal regulation of the cruise ship industry.
"The recent catastrophe with Triumph, the Carnival cruise ship, is just one more mishap for an industry that touts itself as providing safe, family-friendly vacations," Matsui said in a statement provided to The Hill by her office.
"While I am glad that no injuries have been reported, the stranding of almost 4,000 people for four days is anything but safe," she continued. "The power, food and sewage issues reported by passengers are disturbing and raise concerns that these enormous ships are not properly prepared for emergency situations."
Matsui said she hopes Carnival "gets these passengers home to their families safely and swiftly, and that proper investigative and oversight procedures are taken immediately, to ensure that a similar accident does not happen in the future."
Stranded cruise ship's tow temporarily interrupted
By Keith Laing - 02/14/13 10:05 PM EST