Captain Francesco Schettino, who is accused of suspected manslaughter and of abandoning the ship before everyone else was safe, appeared to have cruised too close to land. Witnesses claim he wanted to show the island to a Giglio native, saying "Look, there's your island".
The Costa Crociera company, which owns the Costa Concordia vessel, admitted that Schettino "made an error of judgment which has had serious consequences".
"The route followed by the ship was too close to the coast and it seems decisions in emergency management have not followed procedures in line with those followed by Costa Crociere which in some cases go beyond international standards," said a statement released late on Sunday.
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."
The 52-year-old captain also denied claims that he left the Costa Concordia before evacuation was complete. But a French couple said they saw the captain in a lifeboat before all passengers escaped from the ship. According to Italian navigation code, a captain who abandons a ship in danger can face up to 12 years in jail.
Meanwhile, emergency teams have found one more body in the partially sunken stricken liner. The death toll has risen to six people, with 16 still missing, according to officials.
Two unidentified elderly men were previously found trapped in a flooded area. Earlier three survivors were found.
Two French tourists and Peruvian crew member were confirmed dead on Saturday. The ship, carrying more than 4,200 people, was on the first night of a Mediterranean cruise when it ran aground in calm conditions.
Poor weather is hampering the search as teams scour the hundreds of submerged cabins and other rooms.