A liner owned by the same company as the Costa Concordia, on which at least 25 people died when it ran aground off Italy last month, was adrift in the Indian Ocean after a fire in the engine room left it without power.
Costa Cruises said the fire on the Costa Allegra had been put out and none of the 636 passengers and 413 crew were hurt. The cause of the fire was still unclear.
A French fishing vessel arrived at the stricken ship late on Monday and was helping it to communicate with the Italian authorities, the Italian coastguard said. Two tugs and a helicopter were expected to arrive on Tuesday.
The giant Costa Concordia capsized on January 13 after hitting rocks off the island of Giglio. Divers and rescue workers are still searching for the bodies of seven people who remain missing.
The much smaller, 29,000-tonne Costa Allegra was sailing some 200 miles southwest of the Seychelles when the fire broke out and it sent a distress signal, the company said.
The ship is drifting with no power, but the situation is calm and the captain has assembled the passengers on the decks of the ship, Giorgio Moretti, the head of Costa Cruises nautical operations, told reporters in a conference call.
There is light aboard ship thanks to an emergency battery but no air conditioning or cooking facilities, so passengers will be given bread, water and some fruit until a helicopter arrives on Tuesday morning with more provisions, Moretti said.
The passengers are from 25 different nations, including four children, with the largest contingents being 127 from France and 126 from Italy. There are 38 Germans, 31 Britons, 13 Canadians and eight Americans on board.
They are protected by nine members of an anti-pirate unit of the Italian navy, a precaution regularly taken on ships in the Indian Ocean.
The ship is not in a high-risk area (of pirates) but we can't be 100 percent sure, said Moretti.
Seas in the area were moderate with winds gusting at 25 knots, the Italian coastguard said in a statement.
Moretti said the ship was stable and there was no risk of it running aground or hitting rock.
A French fishing vessel arrived at the ship at around 2230 GMT (10:30 p.m. BT) on Monday, said Italian coastguard spokesman Filippo Marini.
The fishing vessel will remain with the ship for as long as is needed and other ships are on their way, Marini said.
The situation is totally under control, the passengers are well, the crew is well and there is no critical situation of any sort.
Moretti said it had not yet been decided whether to try to transfer the passengers to other vessels or leave them on the ship until it is tugged to shore, either on the Seychelles or Alphonse Island, some 20 miles away.
Two tugs from the Seychelles are due to arrive on Tuesday afternoon.
Shares of Carnival Cruises, which owns Costa Cruises, fell slightly in London trading after news of Costa Allegra's difficulties and were down 2 percent at 1600 GMT.
A Seychelles coastguard official confirmed that support vessels were on their way but said they would give no further information until authorised by Costa Cruises.
Costa said in a statement that the passengers were all in good health and, having been promptly informed of the situation, were assembled at the muster points as a precaution.
Costa Cruises was accused by some passengers of long delays and a lack of organisation in the evacuation of the Costa Concordia.
That vessel's Italian captain is under house arrest near Naples accused of multiple manslaughter and abandoning the ship before the 4,200 passengers and crew were evacuated.
The Costa Allegra left Diego Suarez in Madagascar on Saturday and had been due to dock in the Seychelles capital of Victoria on Tuesday.
(Additional reporting by Steve Scherer and Roberto Landucci in Rome and George Thande in the Seychelles; editing by Philippa Fletcher)