South Korean and US officials have said the 12-day, largely computer-simulated war games are defensive in nature.
The reported threat came a day after a senior U.S. envoy said ties between the rival Koreas must improve before the United States and North Korea can achieve real progress in their relationship.
Kim, supreme commander of the North's 1.2 million-member military, made the comment during a visit to front-line military units, including one that shelled a South Korean island in 2010, according to the official Korean Central News Agency.
"He ordered them to make a powerful retaliatory strike at the enemy, should the enemy intrude even 0.001 millimeter into the waters of the country where its sovereignty is exercised," KCNA said. It did not say when Kim visited the units.
North Korea has regularly issued such rhetoric against joint South Korean-U.S. military exercises.
KCNA said fears of a war on the Korean peninsula have heightened due to the drills, which it called a "new war of aggression." North Korea's powerful National Defense Commission threatened Saturday to wage a "sacred war" over the exercises.
The units visited by Kim included the army battalion responsible for the 2010 shelling of South Korea's Yeonpyeong Island. KCNA said the unit is "well known to the world as it turned Yeonpyeong Island ... into flames," adding that Kim "highly appreciated the feats" by battalion members.
The artillery bombardment, which killed four South Koreans, raised fears of a bigger conflict on the Korean peninsula. North Korea says the attack was triggered by South Korea's firing of artillery into its territorial waters, while South Korea says the firing was part of routine drills.
On Saturday, U.S. envoy Glyn Davies told reporters in Seoul that he made it clear to North Korean First Vice Foreign Minister Kim Kye Gwan in a meeting in Beijing last week that North Korea should improve its relations with South Korea before Pyongyang and Washington can improve their relationship.
The meeting, aimed at restarting stalled international nuclear disarmament talks, was the first since Kim's father and longtime leader Kim Jong Il died in December. Kim Jong Un has quickly taken over power by assuming a slew of prominent titles previously held by his father.
North Korean First Vice Foreign Minister Kim met with China's chief nuclear envoy, Wu Dawei, and Vice Foreign Minister Zhang Zhijun separately on Saturday to discuss the stalled six-nation nuclear talks, according to the Chinese Foreign Ministry. Further details were not disclosed.
More than three years have passed since the last session of the six-nation talks, which involve the United States, the two Koreas, China, Japan and Russia.
