The president wept as he spoke
South Korean President Lee Myung-bak has vowed to respond "resolutely" to the sinking of a warship last month near the sea border with the North.
Pyongyang has denied any role in the sinking of the vessel, which left 46 sailors dead.
In an emotional speech, the president wiped away tears as he recited the names of the dead and missing men.
He did not mention North Korea but said the South's military would become stronger to prevent similar incidents.
"I, as president, will find out the cause of the Cheonan's sinking in full and in detail," Mr Lee said in a speech broadcast nationally.
By John Sudworth, BBC News, Seoul
The first two years in office have not been easy ones for the South Korean president, but the sinking of a warship, with the loss of so many lives, presents Lee Myung-bak with his biggest test by far.
The government knows that the sense of national grief could easily turn to anger. Whether by design or default, the president's tearful address to the nation, in which he read out the names of all 46 crew men killed or still missing, shows he understands the need for an emotional response.
But it was also an appeal for calm, amid intense, daily speculation in the media that North Korea is to blame. The government has come in for criticism, some of it admittedly political, that its handling of the incident has so far been muddled, even secretive. President Lee once again offered reassurance that the cause will be fully and thoroughly investigated.
But the real challenge may still be to come. What if the international team of investigators does find clear evidence that a North Korean torpedo sunk the Cheonan? Doing nothing is, of course, not an option, but what would the president's promised "unwavering and resolute" response look like? Military retaliation, which would terrify investors and risk further escalation, is highly risky, and North Korea is already subject to strict economic sanctions.
"I will deal with the results in an unwavering and resolute way, and make sure that such an incident will never recur."
After reading out the names of each of the 46 sailors lost in the incident, he said:
"Your fatherland, which you loved, will never forget you."
The Cheonan, a 1,200-tonne corvette, sank after breaking into two on 26 March.
South Korea has carefully avoiding making any statement blaming the North for the incident, but investigators who have been bringing up parts of the ship in recent days have ruled out an onboard accident or explosion.
They said the damage appeared to come from an outside blast.
In recent days officials have suggested that a mine left over from the Korean War could have been to blame. They have also suggested a North Korean torpedo could have sunk the ship.
Australian, Swedish and US experts are helping in the continuing investigation.
North Korea's KCNA news agency issued more denials of any involvement over the weekend.
"The South's puppet military and right-wing conservative politicians are now making a foolish attempt to link the tragedy to us," it said.
"The reason that the South's puppets are claiming the North's involvement is also linked to their foolish efforts to put pressure on us, even by stirring up international opinion in favour of sanctions."
Analysts have said there is little the South could do if it was proved to be an attack from the North as any armed confrontation between the two parts of the Korean peninsula would damage the South's economy.
South Korean Foreign Minister Yu Myung-Hwan said the UN might have to be called in if the North was shown to have been involved.