"The special actions of our revolutionary armed forces will start soon to meet the reckless challenge of the group of traitors," the North's military supreme command said in an English-language notice carried by the country's official Korean Central News Agency.
"Once the above-said special actions kick off, they will reduce all the rat-like groups and the bases for provocations to ashes in three or four minutes, in much shorter time, by unprecedented peculiar means and methods of our own style."
The notice and other North Korean statements described South Korean President Lee Myung-bak as a "rat," making personal attacks against the conservative president, who has pursued a hard-line policy toward Pyongyang.
The latest militaristic warning came in response to Lee's recent comments that Pyongyang claimed have hurt the dignity of the North's new leader Kim Jong-un.
Last week, Lee urged Kim to give up the collective farm system and privatize state-owned agricultural land to help enrich the North and its residents. Lee also called on the young North Korean leader to pay greater attention to the human rights and defector issues.
The notice said the North's targets include Lee and conservative South Korean media, though it did not elaborate on details of the North's possible attacks.
South Korea is within striking distance of North Korea's missiles. Seoul, the South Korean capital city of more than 10 million people, is also within range of North Korea's conventional artillery.
Also Monday, the North's Foreign Ministry warned in a separate report carried by the KCNA that North Koreans "are now eagerly waiting for the issue of an order so that they may mercilessly punish the traitor."
"In case something happens on the peninsula now, the responsibility will entirely rest with traitor Lee," the North's statement warned, without elaborating.
The North has also recently vowed to stage a "sacred war" against South Korea and "blow up" Seoul for insulting its dignity over the rocket launch and the celebrations marking the centennial of the April 15 birth of the country's late founder Kim Il-sung, the grandfather of current leader Kim Jong-un.
Lee said the North's failed rocket launch is estimated to have cost Pyongyang about US$850 million, the equivalent of buying 2.5 million tons of corn for North Koreans.
South Korea expressed deep concern that the North's threats and accusations have worsened inter-Korean ties and heightened tensions. "We urge North Korea to immediately stop this practice," said Unification Ministry spokesman Kim Hyung-suk.
The North has made similar military threats against the South over the past several months, although no actual attack has occurred.
South Korea has repeatedly vowed to powerfully retaliate against North Korea in the event of any provocation as a revenge for the North's two provocations in 2010 that killed 50 South Koreans, mostly soldiers.