As many as 31 Britons are among those stranded onboard the Costa Allegra, which was left adrift in the Indian Ocean after an a fire caused a power failure.
The Costa Cruises-operated vessel has now been taken in tow and is headed toward nearby islands where the 1,000-plus people onboard can be transferred to the Seychelles.
The ship is expected to reach the Desroches Island, near Alphonse Island, south-west of the Seychelles later.
No air conditioning or cooking facilities are presently operation onboard the vessel, after a fire in the engine rooms knocked out the power supply.
Battery power is being used to operate essential equipment.
In total there are 636 passengers and 413 crew on board the Costa Allegra, which left Madagascar on Saturday.
Over 100 Italians, as many French and tens of Austrians, Swiss, Germans and Brits are onboard.
No-one has been injured, officials said.
The ship is from the same fleet as the Costa Concordia, which capsized off the Italian coast in January, killing over 30 people.