Besides the three confirmed dead, the Friday night accident involving the 4,200-passenger Costa Concordia left 20 injured, and 41 passengers and crew members unaccounted for -- though officials said many of the missing may be on shore.
The Italian news agency ANSA said there had been 3,216 passenger and 1,013 crew members from 62 nations on board when the ship struck a submerged rock.
Officer Emilio Del Santo of the Coastal Authorities of Livorno said Capt. Francesco Schettino had been interviewed by investigators in Porto Santo Stefano, CNN reported.
ANSA said Schettino said repeatedly he had not made an error in venturing too close to shore but had hit a rock not shown on maps.
The report said officials were trying to determine why the ship didn't immediately issue a mayday.
"At the moment we can't exclude that the ship had some kind of technical problem," Del Santo said, "and for this reason moved towards the coast in order to save the passengers, the crew and the ship. But they didn't send a mayday. The ship got in contact with us once the evacuation procedures were already ongoing."
At least three bodies were recovered from the sea and at least three others were feared dead after the Costa Concordia went aground, Francesco Paolillo, a coast guard spokesman, told The Daily Telegraph of Britain.
CNN said the confirmed dead were two French tourists and a crew member from Peru.
People scrambled to get into lifeboats, while some swam more than 400 yards to shore and helicopters rescued about 50 people on the deck of the 950-foot long ship.
Photos showed a gash in the hull more than 150 feet long with a huge rock protruding into the ship toward the stern. The ship was partly under water listing more than 80 degrees.
Some of those aboard recalled the panic of the harrowing ordeal that began with a loud bang during dinner, followed by the ship coming to a stop and everything going black. A subsequent announcement over the loudspeaker that the ship was having electrical problems was followed by an order for passengers to put on life vests.
"It was just like something out of the Titanic," one woman said. "You could tell straight away that the ship had hit something and no way was it an electrical fault."
"We were having supper when the lights suddenly went out. We heard a boom and a groaning noise. All the cutlery fell on the floor," Luciano Castro told ANSA.
Fulvio Roccii said the ship "started shaking."
"The noise -- there was panic, like in a film, dishes crashing to the floor, people running, people falling down the stairs," Rocci said.
Cabin steward Deodato Ordona told the BBC the crew told the guests "everything was OK and under control, and we tried to stop them panicking."
When the ship rolled a second time, the captain gave the order to abandon ship, but the steep listing made it difficult to accomplish, the BBC said.
Fabio Costa, who was working in a shop on the ship, told the BBC he could feel the ship hitting something.
"All of a sudden we felt the boat hitting something and everything just started to fall, all the glasses broke and everybody started to panic and run ... . We could only feel that the boat had hit something. We had no idea how serious it was until we got out and we looked through the window and we saw the water getting closer and closer.
"Everything happened really, really fast and we saw the water coming in."
The Costa Concordia was on an eight-day cruise out of Rome. The vessel, operated by Costa Cruises, was built in Italy and has been in service since 2006.
Most of the passengers are Italian, with some German and French nationals, ANSA said.
The cruise ship left the Civitavecchia port near Rome earlier on Friday and had been due to visit Palermo, Cagliari, Palma, Barcelona and Marseille.
A Costa Cruises ship crashed into a dock at the Egyptian Red Sea resort of Sharm al-Sheikh two years ago, killing three members of the crew, the Telegraph said.