Statement comes as hunt for hundreds of missing passengers continues and president meets families of victims.
Divers have recovered 13 more bodies from inside the ferry that sank off South Korea nearly four days ago, bringing the confirmed death toll to 58.
Officials said on Sunday that the bodies were recovered after divers gained access to the inside of the ferry after three days of failed attempts due to strong currents. Three bodies were pulled out of the fully submerged ferry just before midnight.
Details of how they got inside the ship were not immediately clear, the Associated Press news agency reported.
The ferry, carrying 476 passengers, many of them schoolchildren, capsized on Wednesday on a journey from the port of Incheon to the southern holiday island of Jeju.
Around 174 people have been rescued but hopes are fading for the estimated 240 people who remain missing.
The captain of the ferry has been arrested on suspicion of negligence and abandoning people in need. Two other crew members have also been taken into custody, including a junior officer who a prosecutor said was steering in challenging waters unfamiliar to her when the accident occurred.
Shin Won-Nam, the head of the Emergency Management Centre, has told reporters that it could take weeks, if not months to complete the rescue operation.
No sounds have been detected from within the capsized hull, the coastguard told reporters on Saturday.
Relatives of more than 200 missing children have supplied DNA samples to help identify bodies recovered from the water.
Investigations into the sinking, South Korea’s worst maritime accident in 21 years based on possible casualties, have centred on crew negligence, problems with cargo stowage and structural defects of the vessel, although the ship appears to have passed all of its safety and insurance checks.
Investigators say Captain Lee Joon-seok, the ship’s captain, was not on the bridge at the time the ferry, the Sewol, started to list sharply and that a junior officer was at the wheel.
Yonhap said Lee faced five charges including negligence of duty and violation of maritime law.
After his arrest the captain said he ordered people to stay in their cabins because he feared they would be swept out to sea by the current.
Handing over the helm is normal practice on the voyage from Incheon to Jeju, which usually takes 13.5 hours, according to local shipping crew.
The ferry went down in calm conditions and was following a frequently travelled route in familiar waters. Although relatively close to shore, the area was free of rocks and reefs.
Lee has not commented on when he left the ship, although he has apologised for the loss of life.