The company operating a cruise ship that capsized after hitting rocks off western Italy on Friday says the captain may have "committed errors".
He appears to have sailed too close to land and not to have followed the company's emergency procedures, Costa Crociere said in a statement.
Capt Francesco Schettino is suspected of manslaughter, but denies wrongdoing.
At least five people have died but about 15 remain unaccounted for. Divers are trying to find more survivors.
"It seems that the commander made errors of judgement that had serious consequences," Costa Crociere said.
"The route followed by the ship turned out to be too close to the coast, and it seems that his decision in handling the emergency didn't follow Costa Crociere's procedures which are in line, and in some cases, go beyond, international standards," the statement added.
Capt Schettino has been detained on suspicion of manslaughter. The chief prosecutor said the vessel had "very ineptly got close to Giglio".
But Capt Schettino denied any wrongdoing, saying the rocks it hit were not marked on his nautical chart.
"We should have had deep water beneath us," he told Italian TV. "We were about 300 metres (1,000ft) from the rocks more or less. We shouldn't have hit anything."
He also also denied claims by prosecutors that he left the Costa Concordia before evacuation was complete. "We were the last to leave the ship," Capt Schettino said.
The 52-year-old captain has worked for Costa Crociere for 11 years. The company said he joined the company in 2002 as an official in charge of security.
He was made captain in 2006, having been the ship's second-in-command.
Like all captains in the fleet he took part in a continuous programme of training and passed all the required checks, Costa Crociere said.
First officer Ciro Ambrosio has also been detained.
Earlier on Sunday, emergency teams recovered the bodies of two elderly men trapped in a flooded section of the partially submerged Costa Concordia.
The bodies are being taken to the mainland for identification. The discovery brings to five the number of those known to have died.
The ship, carrying more than 4,200 people, was on the first night of a Mediterranean cruise when it ran aground in calm conditions.
Rescue teams are continuing to search some of the hundreds of submerged cabins and other rooms.
Three survivors were found on Sunday. Teams working above the waterline rescued an Italian man - a senior member of the ship's crew - who had suffered a severe leg injury.
He was placed on a stretcher and winched up to a rescue helicopter.
Earlier, a Korean couple who were on their honeymoon were discovered trapped in a cabin. They were brought ashore, dazed but unhurt.
Swimming to safety
On Saturday, officials said two French passengers and a Peruvian crew member had died and another 30 people had been injured.
Italian, German, French and British nationals were among the 3,200 passengers on board. There were also 1,000 crew.
On Sunday morning, UK Foreign Secretary William Hague told Sky News all the Britons - 23 passengers and 12 crew - were now safe and accounted for.
The president of Costa Crociere, Gianni Onorato, said the company would "be working in full transparency with Italian authorities" to understand the causes of the disaster.
Mr Onorato said normal lifeboat evacuation had become "almost impossible" because the ship had listed so quickly. Some passengers had to swim to Giglio.
The survivors have been taken by ferry from Giglio to Porta San Stefano, about 25km (15 miles) away on the mainland.
Some described scenes of chaos, and said the crew had not carried out an evacuation drill by the time disaster struck.