In the amateur footage, a crew member says “everything is under control” and asks passengers to go to their cabins.
It is thought the delay in deciding to abandon the ship may have cost lives. At least 11 people died.
Rescue workers have suspended their search once again after the ship shifted in choppy waters on Friday.
The boat’s movements have twice before hampered the work of rescuers, with the search suspended almost all day on Wednesday.
The ship may have only moved by a metre or as little as a few centimetres, but officials fear it could suddenly slip into much deeper water, says the BBC’s Alan Johnston at the scene.
The Costa Concordia ran aground off Italy’s coast a week ago with some 4,200 people on board.
Twenty-one people are still missing, and hopes to find any of them alive are fading fast.
‘Seated and tranquil’
The latest amateur footage was posted online by Italy’s Rainews24 on Thursday.
In it, a female crew member is heard telling passengers: “We kindly ask you to return to your cabins, or go for a walk in the hall, if you like.”
She says that she is relaying a message from the commander.
“We’ll resolve the electrical problem that we have with the generator. Everything will be fine. If you want to stand here, it’s fine.
“But I’m kindly asking you to go back to your rooms, where you’ll be seated and tranquil. Everything is under control.”
In the audio tape aired earlier on Thursday, a port authority officer is heard asking the crewman about the situation on board, after passengers had reported a huge jolt and been told to put on life vests.
But an unidentified voice from the Costa Concordia replies: “We had a blackout and we are checking the conditions on board.”
“Do you need help or are you staying in the Giglio area for now?” the port official asks.
“Confirmed. We remain here in the area to check the blackout,” the crew member replies, without making any reference to a crash.
Our correspondent says the impression left by the recording is that the crewman failed to give a full account of the gravity of the situation.
The ship’s captain, Francisco Schettino, is under house arrest on suspicion of multiple manslaughter.
The owners say he was sailing too close to Giglio on an unauthorised course.
Prosecutors have also accused him of fleeing the ship before evacuation was complete. He denies the accusations.
However Italian media have said Capt Schettino did admit to making a navigational error.
He told investigators he had “ordered the turn too late” as the luxury ship sailed close to an island, according to a leaked interrogation transcript.
He also reportedly said the crew had decided to sail close to the island to salute a former colleague.
The company that owns the ship, Costa Cruises, has suspended Capt Schettino and withdrawn an offer to pay his legal costs, according to reports.
Italian media have also shown pictures of a Moldovan woman who says she was on the bridge after the ship ran aground. The woman defended Capt Schettino’s actions, in an interview with Moldovan TV.
The reports say investigators are trying to speak to her.
Salvage operators are standing by to start pumping fuel from the ship’s tanks to avoid a potential environmental disaster.