Francesco Schettino, the cruise ship captain accused of steering the Costa Concordia into rocks on the island of Giglio in a reckless bid to "salute" the island, has reportedly said he was ordered to carry out the manoeuvre by ship owner Costa Crociere.

"The salute at Giglio on 13 January was planned and wanted by Costa before the departure from Civitavecchia," Schettino told a judge investigating the collision, according to transcripts leaked to Italian newspaper La Repubblica.

At least 13 people died trying to escape from the vessel as it listed on rocks following the collision. A woman's body was found by divers in a submerged portion of the ship on Sunday afternoon, raising the death toll by one. The captain is being held under house arrest accused of manslaughter, causing a shipwreck and abandoning ship.

Meanwhile the head of the Costa Concordia search operation has warned that "clandestine passengers" may have been on board, complicating the identification of bodies and potentially adding to the number who have died. Franco Gabrielli said: "There could have been X persons who we don't know about who were inside, who were clandestine" passengers aboard the ship." People might have been invited aboard by a staff member as the ship departed and not registered, another official said.

Schettino said the "salute" should have been carried out a week earlier, but was put off due to bad weather.

He reportedly told the investigating judge that there was "insistence" by the firm on carrying out such manoeuvres, because it was a good way to promote its cruises.

"Costa was aware of the repeated practice of 'saluting' around the world," said Schettino.

The claims appeared to contradict Pier Luigi Foschi, the chief executive of Costa Crociere, who said last week: "I can't exclude that ships have been sailed closer to land on the initiative of some captains without informing us. But I have never been aware of this taking place in an unsafe manner."

He said steering within metres of Giglio on 13 January was "unapproved, unauthorised and unknown to Costa" and pointed to the onboard newspaper, which said the ship would stay five miles off the coast.

Schettino said he had given up-close salutes to the island of Capri and the Sorrento coast near Naples on previous occasions, as well as at Giglio, following the example of another Costa captain.

One US law firm which is preparing legal action on behalf of passengers has said: "It's too easy to say this captain acted alone."

In response to Schettino's latest claims, Costa Crociere said on Sunday: "Costa Crociere will not be commenting on any aspect of the ongoing judicial proceedings."

Schettino also reportedly told the judge, Valeria Montesarchio, that on the night of the collision he discovered some of the equipment which records navigation data was out of order, which could hamper investigators' efforts to reconstruct his route.

The transcript also shows Schettino at odds with Costa's account of the communication between captain and company after the collision.

Foschi has accused Schettino of keeping the firm in the dark about the state of the ship, which was listing as it took on water.

Schettino reportedly told the judge he gave an accurate description of the collision to Costa Crociere official Roberto Ferrarini and told him he would seek to swing the boat around on to rocks by Giglio port.

"Yes, do that," Schettino reports Ferrarini telling him. And when the boat grounded, Ferrarini allegedly said "At this point, more than this … We won't sink any longer."

In an interview with French newspaper Le Figaro, Foschi said Schettino had always been considered one of the firm's best captains, albeit with a "pronounced ego".

On the island of Giglio, the head of Italy's civil protection agency Franco Gabrielli arrived on Saturday to take over the search for passengers left on board the listed vessel after mounting concern over the duplication of efforts – and the conflicting information given out by – the various police, military and emergency services who have been involved.

Gabrielli may decide that salvage teams can now start working on removing fuel from the vessel even as the search for passengers continues, suggesting that the Dutch salvage workers waiting on Giglio could have been sent into action days ago.

Fears are growing that the ship could slip into deeper waters, even though the predicted arrival of bad weather that could disturb the Costa Concordia is now thought to be further off.

Over the weekend, ferries to Giglio from the mainland were filled with tourists keen to see the marooned Costa Concordia. Some of them took picnics on to the rocks overlooking the vessel.