The captain who grounded the Costa Concordia off the Tuscan coast with 4,200 people on board did not relay correct information either to the company or crew after the ship hit rocks, the cruise ship owner's boss said as the search resumed for 21 missing passengers.

Chief executive Pierluigi Foschi told Italian state TV that the company spoke to the captain at 10.05pm, some 20 minutes after the ship ran aground on January 13, but could not offer proper assistance because the captain's description "did not correspond to the truth".

Captain Francesco Schettino said only that he had "problems" on board but did not mention hitting a reef.

Likewise, Mr Foschi said crew members were not informed of the gravity of the situation.

Passenger video shown on Italian TV indicates crew members telling passengers to go to their cabins as late as 10.25pm. The abandon ship alarm sounded just before 11pm.

"That's because they also did not receive correct information on the gravity of the situation," Mr Foschi said.

The £290 million Costa Concordia was carrying more than 4,200 passengers and crew when it slammed into well-charted rocks off the island of Giglio. Eleven people have been confirmed dead.

The Concordia shifted again on its rocky perch yesterday, forcing the suspension of diving search operations for the 21 people still missing and raising concerns about the stability of the ship's resting place. But the search in areas above the waterline resumed in the evening after the ship was deemed stable.

The remarks by Mr Foschi are the latest to indicate a lack of proper communication with authorities on land as the emergency unfolded.

An audiotape of the Concordia's first contact with maritime authorities has a Concordia office repeatedly replying that the ship had experienced a blackout, even though it had hit the reef more than half an hour earlier.

Italian media reported the officer on the call was Schettino, but that could not be independently confirmed.

Costa Crociere, which offered support to the captain in the hours after the emergency, has now turned its back on the man who is under investigation for manslaughter, causing a shipwreck and abandoning his ship.

Schettino, who was jailed after he left the ship, is under house arrest near Naples.

Costa in recent days has suspended Schettino, announced it is no longer paying his legal fees and has signed on as a civil party in the prosecution, a move that positions it as an injured party and would allow it to seek damages in the case of a guilty verdict.

Coastguard spokesman Cmdr Cosimo Nicastro said crews would evaluate the ship's stability this morning to see if the diving operation could resume, focusing on an area where passengers would have sought lifeboats.

It was not clear if the slight movements registered by sensors placed on board the Costa Concordia were just vibrations as the ship settles on the rocks off the Tuscan island of Giglio or if the massive ocean liner is slowly slipping off the reef. Salvage experts suggest it could be because of pockets of air gradually escaping.

The sensors detected that the ship's bow was moving about 15mm an hour and the stern about 7mm an hour, said Nicola Casagli of the University of Florence, who was called in by Italian authorities to monitor the ship's stability.

The Concordia's movements are being watched since any significant shift could be dangerous for divers trying to locate those missing since the Concordia ran aground January 13. An additional fear is that movement could damage tanks holding a 500,000 gallons of fuel oil and lead to leaks.

The sea floor drops off sharply a few yards from where the ship is resting, and Italy's environment minister has warned it risks sinking.

Yesterday, relatives of some of the 21 missing were at Giglio's port getting briefings from rescue teams.

Mr Casagli told Sky TG24 that some movement in the Concordia was only natural given the immense weight of the steel-hulled ship, which is being held in place by two huge rocks at bow and stern.

But the latest movements indicate it isn't stable, he said. "These are small, regular movements that are being monitored because they're going in the same direction," he said.

On Thursday, Carnival, the US-based company that owns Costa, announced it was conducting a comprehensive audit of all 10 of its cruise lines to review safety and emergency response procedures in the wake of the Costa disaster.

The evacuation was chaotic and the alarm to abandon the ship was sounded after the Concordia had capsized too much to get many life boats down.