Rescue teams searching the stricken Italian cruise liner Costa Concordia recovered a woman's body from the wreckage Sunday, taking the death toll from the disaster to 13.

The victim was found wearing a life jacket near the stern on the seventh of the vessel's 17 decks, ANSA reported.

She becomes one of five bodies yet to be identified. Four French nationals, a German, a Hungarian, a Spaniard and an Italian were confirmed to have died so far, according to the Italian gendarmerie.

The search for bodies resumed Sunday after the vessel earlier shifted on the sea ledge on which it is resting. The capsized ship has been lying on its side near the island of Giglio since running aground at 9:45pm local time Jan. 13.

Pierluigi Foschi, the CEO of the company that owns the cruise ship, met with the families of the missing Sunday during a brief visit to the island, Sky Italia's TG24 reported.

Twenty-four people remained listed as missing, including Minnesota couple Jerry and Barbara Heil, though that figure could fall to 19 once the five unidentified bodies are named, after DNA tests.

Relatives of the Heils were taken by the Italian authorities to an area near the Costa Concordia, where they placed daisies and white roses in the water Saturday.

The most recent missing passenger known to have survived was German woman Gertrud Georgens, who turned up alive back in her home country Wednesday.

There were roughly 4,200 people on board the $450 million ship when it capsized.

The vessel's captain, who has been accused of abandoning ship when it hit rocks, reportedly admitted to his bosses that he "messed up," though he initially claimed to have done all he could to assist passengers in the wake of the disaster.

Francesco Schettino, who is under house arrest near Naples, faces charges of manslaughter and abandoning ship after he allegedly left the cruise liner before hundreds of passengers. Schettino claims that he tripped and fell into a lifeboat.

Cruise company chief Foschi previously told Italian state TV that the company was not able to offer appropriate aid at the time because Schettino's description of events 20 minutes after running aground -- that he had "problems" on board -- "did not correspond to the truth" and made no mention of hitting the reef.

Foschi also alleged that crew members were not informed of the gravity of the situation, which led to some passengers being told to go back to their cabins 40 minutes after the collision. A further 35 minutes passed before the abandon ship alarm sounded, just before 11:00pm local time.

Divers salvaged a hard disk from the ship that might have video footage from security cameras on the ship's bridge and could potentially shed some light on the captain's actions during the accident, AFP reported.

The Costa Concordia also was said to be leaking light fuel, which could damage the Tuscan marine sanctuary in which it capsized.