A statement from North Korea's military command said the targets include Lee and South Korean media, but it did not reveal details of the possible attacks, South Korea's Yonhap News Agency reported.
The "special actions of our revolutionary armed forces will start soon to meet the reckless challenge of the group of traitors," the statement said.
"Once the … special actions kick off, they will reduce all the rat-like groups and the bases for provocations to ashes in 3 or 4 minutes ... by unprecedented peculiar means and methods of our own style," it said.
The threat was one of several statements issued by North Korean officials that made personal attacks against Lee, a conservative president who has pursued a hard-line policy toward his northern neighbor.
In another statement, reported by North Korea's official Korean Central News Agency, the Foreign Ministry called Lee a "traitor [who] let loose a string of such malignant invectives" against Pyongyang over money spent to commemorate the centennial birth of President Kim Il Sung that Lee said should have been used to buy food for the impoverished nation.
"Lee is no more than human scum of the times as he so malignantly desecrated this significant holiday, far from congratulating the compatriots in the North on it," the news agency said.
That commentary also said any provocative action would come from Seoul.
"The situation on the peninsula is so tense that it may go beyond control due to the desperate frenzy of the traitor on the deathbed," the statement said. "In view of the prevailing situation, the [North Korean] Foreign Ministry solemnly declares that in case something happens on the peninsula now, the responsibility will entirely rest with traitor Lee."