North Korea has flatly denied the allegation and warned that any retaliation by the South would trigger war on the peninsula.
The UN Security Council is expected to meet in New York later on Monday to discuss a South Korean request for further sanctions against the North over the sinking.
According to the foreign ministry in Seoul, North Korea also planned to address the council about the sinking.
Relations between North and South Korea have plunged to their lowest level in years following the incident.
South Korea has already taken a number of punitive measures against North Korea, including resuming cross-border propaganda broadcasts that were suspended in 2004.
North Korea has said it will blow up banks of loudspeakers being built by South Korean soldiers along the heavily-fortified frontier.
At the weekend a statement from North Korea's military command threatened to turn the South Korean capital into a "sea of flame".
In his speech on Monday Lee also said he would hold some South Korean naval officers responsible for the sinking of the Cheonan, although he not specify who.
His comments came a day after South Korea's top military officer offered to retire amid criticism over alleged negligence ahead of the sinking.