The KCNA report said Mr Kim declared a “semi-state of war” at an emergency meeting late Thursday.
It threatened action unless Seoul ends its anti-Pyongyang border broadcasts.
The North often uses fierce rhetoric when tensions rise and it has made similar declarations before.
The BBC’s South Korea correspondent Steve Evans says that although this ritual of aggression often sees such language escalate to the firing of ammunition, this time the rhetoric is fiercer and artillery shells are now in use.
KCNA reported that Mr Kim had ordered that troops be “fully ready for any military operations at any time” from 17:00 Friday local time (08:30 GMT), at the emergency meeting of the central military commission.
South Korea’s Vice Defence Minister Baek Seung-joo said that 11 sites with loudspeakers for the anti-Pyongyang broadcasts are likely to be targets.
South Korea’s Yonhap news agency, citing a government source, said that North Korea appeared to be preparing to fire missiles.
The North often conducts missile tests to show displeasure at South Korea, or in protest at US-South Korean military drills.
In 2004, South Korea and North Korea reached an agreement to dismantle their propaganda loudspeakers at the border.
The broadcasts were part of a programme of psychological warfare, according to South Korean newspaper Korea Times, to deliver outside news so that North Korean soldiers and border-area residents could hear it.
Military authorities say days later the North also restarted its broadcasting of anti-South propaganda.
However, some reports said that the quality of the North Korean loudspeakers is so bad that it is difficult to understand what they are saying.
The latest tensions come after North Korea fired a shell at South Korea’s western border on Thursday, reportedly to protest against the South’s propaganda broadcasts.
The South responded to the North’s shelling with artillery fire, and ordered the evacuation of some of its residents on the border. There were no reported casualties.
North Korea then warned the South that it would take military action unless border propaganda broadcasts were ended and broadcast facilities dismantled “within 48 hours”.
However, in a separate letter Pyongyang said it was willing to resolve the issue even though it considered the broadcasts a declaration of war, South Korea’s unification ministry said, according to Reuters.
North Korean media outlets used a mixture of new and old phrases on Friday to warn the government in Seoul. KCNA news agency announced that the country was in “a state of semi-war in the frontal zone”.
State-run media outlets often reminisce how founding President Kim-Il-sung declared a state of “semi-war” against the “gangster-like” attitude of the US in the 1990s.
In the current crisis, phrases like “puppet forces”, “war maniacs”, “hostile and hooligan army” and “psychological warfare” have also been use by the media.
State-run radio said South Korea had launched a “vicious political and military provocation” against Pyongyang. It added that such provocations were “currently driving the country’s situation toward the phase of exploding into a critical point”.
Another report by KCNA said that such “foolhardy provocation deserves harsh punishment”.
The two Koreas remain technically at war, because the 1950-1953 war ended in an armistice, not a peace treaty.
South Korea and the US also began annual joint military exercises on Monday – they describe the drills as defensive, but North Korea calls them a rehearsal for invasion.