Two French nationals and a Peruvian died after the Italian-owned cruiser ran aground near the island of Giglio off the Tuscan coast on Friday night.
But this evening, as search and rescue teams battled failing light, the coastguard said the bodies of two elderly passengers were found by divers in a section of the submerged restaurant.
The news came just hours after a honeymooning South Korean couple were found alive, and a cabin services director was also rescued despite suffering a suspected broken leg.
Officials reduced the initial number of missing from 70 to 17 - six crew and 11 passengers.
Thirty people were said to be injured, two seriously.
Foreign Secretary William Hague confirmed that the Britons, 23 passengers and 12 crew, were safe and well and being helped by officials to return home.
Speaking on Sky News, Mr Hague said: “We can say now, on the basis of the information available to us, that all the British nationals involved are accounted for and are safe.”
He added: “They have been through a very dreadful and distressing experience so we'll do all we can to look after them. That is our prime concern in a case like this, to make sure British nationals are safe and looked after.”
As pressure for an explanation of how the huge cruiser could crash into rocks intensified, the Concordia captain, Francesco Schettino, told Italian television he had not expected the rocks to be in the area where the ship ran aground.
He said: “I don't know if it was detected or not, but on the nautical chart it was marked just as water and some 100-150 metres (328ft-492ft) from the rocks, and we were about 300 metres (984ft) from the shore, more or less.
“We shouldn't have had this contact.”
Cpt Schettino and an officer were held and questioned by prosecutors on suspicion of multiple manslaughter, abandoning ship, and causing a shipwreck, state TV and Sky TV said.
But tonight one maritime expert said it was important the captain was given “leeway” and time to explain his decisions.
Karen Jacques, chief operating officer, of Dryad Maritime, which provides risk forecasts and advice to mariners, said: “It's his ship that's sinking and he will feel that in his belly.”
Police divers and rescue crews continued to circle the wrecked ship which sustained a massive gash after crashing into rocks.
Crews in dinghies examined the ship near the site of the 160-foot hull hole where water flooded in and caused the ship to lurch to its side.
Survivors said the terrifying, chaotic escape was like a scene from the Titanic which went down 100 years ago claiming 1,517 lives.
Many passengers complained the crew did not give them good directions on how to evacuate.
They also claimed that once it became clear it was an emergency there was a delay lowering the lifeboats until the ship was listing too heavily for many to be released.
Several other passengers said crew members told passengers for 45 minutes that there was a simple “technical problem” that had caused the lights to go off.
Angry passengers also claimed they never participated in an evacuation drill, although one had been scheduled for yesterday.
Cruise bosses defended the actions of the crew and said they were co-operating with the investigation.
Survivor John Rodford said staff gave him and his wife incorrect information as the drama unfolded while they were dining.
“They said 'No, it's all right, it's just a malfunction in the engines,” he told Sky News.
“Then it started tilting the other way and the plates came off the tables.”
He said passengers scrambled for lifejackets and he and his wife slid across the deck to find a lifeboat.
Mr Rodford said an evacuation drill was scheduled for the day after the cruise went down.
Reliving his escape, he said it was “chefs and waiters” helping passengers flee rather than officers.
He said: “The people who served us our dinner, were the people who helped us get on the lifeboats and were manning the lifeboats.
“I didn't see captains' jackets and things like that. It was dinner staff.”
He added that when it came to getting him off, the “Costa people are far and few between to be honest - very scarce”.
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