Lee Myung-bak is facing growing domestic pressure to take a tougher line against the North over the incident.
"We cannot afford to have a slightest mistake and will be very prudent in all response measures we take"
South Korean president
However speaking during the meeting in Seoul on Friday he said South Korea would be prudent in responding to North Korea's "military provocation".
"Since this case is very serious and has a grave importance, we cannot afford to have a slightest mistake and will be very prudent in all response measures we take," Lee was quoted as saying.
Forty-six South Korean sailors were killed when the patrol ship Cheonan was hit by an explosion, broke in two and sank in the Yellow Sea off the west coast of the Korean peninsula.
The ship was later salvaged from the sea bed and is in dry dock at a naval base south of Seoul.
South Korea has made clear it has no plans for a retaliatory strike, saying instead it will press for more sanctions against Pyongyang.
It also wants the North to be returned to the US list of state sponsors of terrorism.
On Thursday the US warned that North Korea would face "consequences" for what it said was the "unprovoked and unwarranted" attack on the Cheonan.
|The sinking has sparked protests in South Korea with calls for a tough response [Reuters]
"Clearly this was a serious provocation by North Korea and there will definitely be consequences because of what North Korea has done," PJ Crowley, spokesman for the US State Department, told reporters.
Crowley's comments followed the release in Seoul of a report by a multinational investigation team which concluded there was overwhelming evidence that the Cheonan was sunk by a torpedo fired from a North Korean submarine.
The investigation team included experts from the US, Britain and Sweden.
The team's report said Korean markings found on salvaged parts from the torpedo matched markings on a stray North Korean torpedo recovered by the South seven years ago.
Pyongyang has condemned the report as a "sheer fabrication", accusing the South's conservative government of using the incident for political gain and to worsen already chilly ties between the two Koreas.
North and South Korea remain technically at war having never signed a formal peace treaty to end the 1950-53 Korean War.
According to the investigation report released on Thursday the Cheonan was split apart by a shockwave and bubble effect produced by the underwater explosion of a torpedo.
|Investigators said recovered remains were identical to a North Korean torpedo [AFP]
It said torpedo parts recovered including the propellers, propulsion motor and a steering section "perfectly match the schematics of the CHT-02D torpedo shown in brochures provided to foreign countries by North Korea for export purposes".
"The evidence points overwhelmingly to the conclusion that the torpedo was fired by a North Korean submarine," the joint civilian and military investigation team said.
"There is no other plausible explanation."
Intelligence gathered with the South's allies - the US, Britain and Australia - showed North Korean submarines were likely in operation near the scene of the sinking, with similar vessels of other neighbouring countries all inside their territorial waters.
"Based on all such relevant facts and classified analysis, we have reached the clear conclusion that the Cheonan was sunk as a result of an external underwater explosion caused by a torpedo made in North Korea," the report said.
The ship was sunk while it was on what South Korean officials said was a routine patrol mission in an area of the Yellow Sea that is claimed by the North.
The area was the scene of deadly clashes in 1999 and 2002 and of a firefight last November that left a North Korean boat in flames.
North Korea has said it plans to send its own investigators to the South to look into the causes of the sinking.
But South Korea's Yonhap news agency on Friday quoted a source in the South's defence ministry as saying it had no intention of allowing such a delegation.