About 40 people were still missing on Sunday more than 24 hours after an Italian cruise ship with more than 4,000 on board capsized off Italy's west coast, killing at least three people and injuring 70.

The captain of the luxury 114,500-tonne Costa Concordia was being held in jail accused of multiple manslaughter, causing a shipwreck and abandoning ship, Italian police said.

Passengers, some saying it felt like a rerun of the Titanic disaster, told of people leaping into the sea and fighting over lifejackets in panic when the ship hit a rock and ran aground near the island of Giglio late on Friday.    

"I was sure I was going to die. We were in the lifeboats for two hours, crying and holding on to each other," said Antonietta Sintolli, 65, breaking down in tears as she recounted the event. "People were trying to steal lifejackets from each other. We could only gets ones for children."

Passengers said the mainly Asian crew members, few of them able to speak Italian, were slow to respond to the disaster and struggled to bring order to the evacuation.

Early on Sunday, firefighters found two people, both South Koreans, still alive in a cabin after making voice contact with them from several decks above, Italian media reported.

An official involved in the rescue operation said two French tourists and a Peruvian crew member were dead.

There were fears the death toll could rise in one of Italy's worst shipping disasters in years as specialist diving teams checked interior spaces of the vessel.

"We don't rule out the possibility that more people will be lost," said fire services spokesman Luca Cari. It was not clear how many of those unaccounted for could still be trapped in the ship or simply had not been counted among those rescued.

The ship's captain, Francesco Schettino, was arrested on Saturday night for questioning by magistrates, police said. They said Schettino, whose ship was carrying 4,229 passengers and crew, abandoned the vessel before all the passengers were taken off.   

The vessel's operator, Costa Crociere, a unit of Carnival Corp & Plc, the world's largest cruise company, said the Costa Concordia had been sailing on its regular course when it struck a submerged rock.

In a television interview, Schettino said the rock was not marked on any maritime charts of the area. Costa Cruises president Gianni Ororato said the captain "performed a manoeuvre intended to protect both guests and crew" but it was "complicated by a sudden tilting of the ship".

It remained unclear how the 290-metre long ship had run aground in calm waters so close to the shore. "We'll be able to say at the end of the investigation. It would be premature to speculate on this," said coastguard spokesman Filippo Marini. - Reuters