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The head of the Italian coastguard, Marco Brusco, said "a glimmer of hope remains" of finding survivors and that fire brigade crews would work on the ship through the night in their increasingly desperate search.
He said four crew members and 25 tourists including six Italians remained unaccounted for, revising sharply upward an earlier estimate of 15.
"It's dangerous work," he said, as divers and mountain rescue teams spoke of the difficulties of operating in the half-submerged ship.
The earlier figure for the missing did not take into account at least 10 Germans that a German official said were unaccounted for Monday. American and French tourists are also among the missing, as well as crewmen.
The death toll also rose to six after divers found the body of a man in the early hours of Monday.
Three of the victims -- two Frenchmen and one Peruvian crew member -- drowned after jumping into the chilly Mediterranean waters along with dozens of others in a chaotic evacuation in the Friday the 13th tragedy.
Rodolfo Raiteri, head of the coastguard's diving team, told AFP on the shore: "The conditions inside are disastrous. It's very difficult. The corridors are cluttered and it's hard for the divers to swim through."
But the local mayor also voiced hope of finding more people alive.
"You never know in the labyrinth of that ship. An air pocket could have allowed people to survive a few days," mayor Sergio Ortelli told AFP.
Choppy seas forced a temporary evacuation of the stricken 17-deck Costa Concordia for several hours after the half-submerged ship slipped on a rocky shelf under the sea, sparking fears that the giant hulk could sink entirely.
Ortelli warned that the stricken vessel, which hit rocks and keeled over off Giglio Island, was an "ecological timebomb" in the pristine waters of a marine nature reserve.
Environment Minister Corrado Clini said a state of emergency would be declared this week to drum up funds and beef up rescue and clean-up operations in case of an environmental disaster.
The head of the company that owns the vessel said it had hit a rock as a result of an "inexplicable" error by the captain, Francesco Schettino, who was arrested on Saturday along with first officer Ciro Ambrosio.
"He carried out a manoeuvre which had not been approved by us and we disassociate ourselves from such behaviour," said Pier Luigi Foschi, the boss of Costa Crociere, Europe's largest cruise operator.
But Foschi also paid tribute to the other crew members, saying they had "all behaved like heroes".
Schettino was under special surveillance in Grosseto, the main town in the area.
"He has not shown any suicidal tendencies but it is clear that he is going through a very delicate period which requires special attention," a prison official said.
Italian prosecutors accuse the two officers of multiple homicide and abandoning ship before all the passengers were rescued.
A transcript of a conversation between Schettino and a port official was released Monday showing that the captain refused to return to the ship to oversee rescue operations.
"Now you go to the bow, you climb up the emergency ladder and coordinate the evacuation," the official tells Schettino, according to the transcript of the conversation recorded on one of the ship's "black boxes" recovered by rescuers.
"You must tell us how many people, children, women and passengers are there and the exact number of each category," he said.
"What are you doing? Are you abandoning the rescue? Captain, this is an order, I am the one in charge now. You have declared abandoning ship," the port official said.
Investigators on Sunday also started analysing the "black box" for precise details of the ship's movements.
"It's clear that the captain underestimated many aspects and did not stay the course," said Filippo Marini, a spokesman for the Italian coast guard.
The Costa Concordia was carrying more than 4,200 people when it ran aground shortly after starting a seven-day Mediterranean cruise on its way to Marseille in France and Barcelona in Spain, just as many passengers were having dinner.
Carnival Corp, the parent company of Costa Crociere, put the initial cost of the disaster at $85-95 million (67-75 million euros).
Island residents have already said the ship was sailing far too close to Giglio and had hit a reef known as the School Rocks, well known to inhabitants.
The Corriere della Sera reported Monday that the captain had passed close to the island's rocky shores to please the head waiter who comes from Giglio.
It also quoted witnesses as claiming the waiter had warned Schettino just before the accident happened: "Careful, we are extremely close to the shore."
Crews on Monday began putting down anti-spill booms as fears of a leak rose and local officials called for strict curbs in the future on shipping routes through an area of outstanding natural beauty.
Passengers meanwhile described confusion on board as the lights went out and how they were at first told it was just an electrical fault -- before the ship lurched sharply on to its side and panic set in.
Rose Metcalf, a 23-year-old crew member, wiped away tears as she told how she wrote a note to her mother in case she did not survive.
"There was absolute panic. It was just terrifying, I was just trying to keep people calm. People were white, people were crying, screaming," she told BBC television on her return to England.
Ennio Aquilino, a fire brigade chief who was one of the first on the scene and still bore the scars from a fall during the rescue operation, said it had been "an apocalyptic scene".