The fire in the aft engine room knocked out the ship's propulsion system. The ship has been operating on backup generator power since the incident, the statement said.
When another Carnival cruise ship, the Legend, rendezvoused with the stranded vessel Monday, Texas resident Brent Nutt was able to briefly chat with his wife, Bethany, who could draw a cellphone signal from the visiting cruise line.
Without power, the ship's stabilizers are apparently not working, Nutt told The Associated Press, and the massive liner had been leaning to one side Sunday. By Monday afternoon, the ship seemed more upright, he said.
"She sounded a whole lot better today than she did yesterday," Nutt said about two hours after chatting with his 32-year-old wife.
Oliva said the "very slightly" 4.5-degree list was caused by the 25-knot winds from the south-southeast, a condition not unexpected "given the wind speed and posed no safety risk."
It wasn't immediately certain if the list had been corrected with the ship under tow.
Nutt said his wife told him passengers were also given food and some of the bathrooms are working. But the ship is dirty, he said his wife told him.
"There's water and feces all over the floor," Nutt relayed. "It's not the best conditions. You would think Carnival would have something in place to get these people off the ship."
Passengers also are getting sick and throwing up, he said, adding that his wife told him: "The whole boat stinks extremely bad."
A similar situation occurred on a Carnival cruise ship in November 2010. That vessel was also stranded for three days with 4,500 people aboard after a fire in the engine room. When the passengers disembarked in San Diego they described a nightmarish three days in the Pacific with limited food, power and bathroom access.
Carnival said in a statement that it had cancelled the Triumph's next two voyages scheduled to depart Monday and Saturday. Passengers aboard the stranded ship will also receive a full refund, the statement said.