Filing for themselves and other passengers, Matt and Melissa Crusan of Oklahoma alleged that "Carnival knew or should have known that the vessel Triumph was likely to experience mechanical and/or engine issues because of prior similar issues," CNN reported Thursday.
The lawsuit, filed earlier this week in U.S. District Court in the Southern District of Florida, alleged that conditions on the ship "created a severe risk of injury, illness and/or disease."
Carnival spokesman Vance Gulliksen said the company was "unable to comment on pending litigation."
On Feb. 7, the Triumph left Galveston, Texas, for a four-day cruise to Mexico, but on the third day, a fire broke out Feb. 10, ending the trip. The vessel was carrying more than 4,200 people, including 3,100 passengers, and conditions deteriorated as human waste overflowed into public spaces on the ship.
Tug boats pulled the disabled ship to Mobile, Ala., Feb. 14. The disembarking ended Feb. 15.
On Tuesday, the U.S. Coast Guard said a leak in a fuel-oil return line running from one of the ship's engines was the cause of the fire.
In the lawsuit, the Crusans said they and other passengers "were harmed and/or injured" because of the fire and being stranded at sea without necessary services and supplies from Feb. 10 through Feb. 15.
They were given "spoiled and rotting food" to eat, the lawsuit said, and "sewage and/or human waste sloshed around the vessel as the vessel listed while drifting and/or while under tow."
Another lawsuit was filed against Carnival last week.