More than 3,100 stranded passengers are slowly making their way to port following a fire on board Carnival Cruise Lines’ Carnival Triumph.

A fire that ignited in the cruise ship’s engine room early Sunday took out the vessel’s propulsion system leaving passengers and 1,086 crew members adrift in the Gulf of Mexico about 150 miles off the Yucatan Peninsula.

No one was injured and the fire was extinguished. The ship has been operating on backup generator power since the incident.

The first of two tugboats arrived Monday to escort the ship to port. Based on the ship’s location after drifting overnight, officials scuttled original plans to tow the vessel to Progreso, Mexico aiming, instead, for Mobile, Ala. where it is expected to arrive sometime Thursday.

In the meantime, passengers report miserable conditions, including a lack of running water, few functional toilets and long lines for food. With the ship’s air-conditioning system out of commission, some passengers opted to spend the night on deck to keep cool.

On Monday, Carnival issued a statement: We have maintained constant contact with the ship’s officers.  All of our guests are safe, and we’re doing everything we can to make them as comfortable as possible. The ship has maintained emergency generator power since the fire occurred and the technical team on board has been successful in gradually restoring auxiliary power to operate some basic hotel functions. Currently, public and cabin toilets are operational in certain sections of the ship, power has been restored to a limited number of elevators, and some power in the Lido dining area is providing for hot coffee and limited hot food service.

Carnival will offer a full refund to all guests on the ill-fated cruise, including transportation expenses. In addition, they will receive a credit equal to the fare paid for a future cruise and reimbursement for all shipboard purchases during the voyage, with the exception of gift shop and casino charges. The ship’s next two scheduled departures have been canceled.