The ship, the Carnival Triumph, is at least a day from being guided to a port in Alabama.
Carnival President Gerry Cahill said the ship has running water and most of its 23 public restrooms and some of the cabin bathrooms were working. He said the ship has not seen an abnormal number of people reporting illnesses.
Some passengers aboard the ship have complained to their relatives of filthy, hot conditions and limited access to food.
Jimmy Mowlam, 63, whose 37-year-old son, Rob Mowlam, got married Saturday onboard the ship, said his son told him by phone Monday night that there is no running water and few working toilets. He said passengers were given plastic bags to "use for their business."
The vessel is being towed by tug boats to Mobile, where it is estimated to arrive on Thursday.
The ship left Texas for a four-day cruise last Thursday with 3,143 passengers and 1,086 crew members. The Triumph was about 150 miles off Mexico's Yucatan Peninsula on Sunday when an engine room fire blew out its primary power source, crippling its water and plumbing systems and leaving it adrift on only backup power.
No one was injured in the fire, but Carnival spokeswoman Joyce Oliva said Tuesday that a passenger with a pre-existing medical condition was taken off the ship as a precaution. Everyone else likely will have to remain onboard until the ship reaches Alabama.
Oliva said the company has yet to determine what caused the fire. The National Transportation Safety Board announced Tuesday it has opened an investigation into the cause of the blaze.
Oliva also said Carnival has reserved more than 1,500 hotel rooms in Mobile and New Orleans for Thursday. The company plans to return passengers back to Houston on Friday using charter flights. Passengers aboard the stranded ship will also receive a full refund.
The Associated Press contributed to this report.