Italian coastguard official Marco Brusco said 25 passengers and four crew members remain unaccounted for three days after the vessel crashed into a reef off the Tuscan coast near the island of Giglio. Six people have been confirmed dead.
At least three Italian families have said that although their loved ones were listed among those safely evacuated, they have not heard any word from them. About 10 Germans are thought to be among those unaccounted for.
Mr Brusco said he held a "glimmer of hope" that some of the missing might have survived, but Giglio mayor Sergio Ortelli said earlier that hopes of finding any of them alive are minimal. He told the Italian press that the only hope is that bubbles of air had formed within the ship after it hit the rocks.
The operator of the Costa Concordia cruise liner blamed the captain for sailing close to land to "show the ship to the port".
The chairman of Costa Cruises said the unauthorised deviation from the route had been taken to "make a salute". Pier Luigi Foschi has apologised for the tragedy which has left dozens of people injured and the 114,000-tonne Costa Concordia lying on its side off Tuscany.
At the centre of the investigation into the disaster is the liner's captain, Francesco Schettino, who is being investigated by prosecutors for possible manslaughter, abandoning ship and causing a shipwreck. He has been accused of leaving the vessel before ensuring that all of the 4,200 people aboard, including 35 Britons, were safely evacuated.
Mr Schettino insisted in an interview before his jailing that he stayed with the vessel to the end. Mr Schettino, who has commanded the ship since it was built in 2006, has said that nautical charts did not show the rocks off the tiny island of Giglio.
The search for any survivors continued until it had to be suspended in early afternoon after the vessel shifted a few inches in rough seas. Later, with the weather improving, the search resumed.
Costa Cruises are concerned about the 500,000 gallons of fuel on board which are in 17 separate tanks. It is feared that any further movement of the ship could cause some of it to leak into the water.