The firings were aimed at sending a "solemn warning to South Korean military warmongers who are introducing ultramodern offensive weapons into South Korea and pushing to hold (a) military exercise in defiance of the repeated warnings from the North", reported the Korean Central News Agency (KCNA).
On Thursday, North Korea launched two missiles from Hodo Peninsula near the North's eastern coastal town of Wonsan. One of them was a "new type of tactical guided weapon" launched under the supervision of Kim.
South Korea's Joint Chiefs of Staff said on Friday that both flew around 600 km, modified from an earlier estimate that they travelled 430 km and 690 km, respectively, Yonhap news agency reported.
After watching the launches, Kim expressed satisfaction over "the rapid anti-firepower capability of the tactical guided weapon system and the specific features of the low-altitude gliding and leaping flight orbit" of the missile, which would be hard to intercept, the KCNA said.
"It must have given uneasiness and agony to some targeted forces enough as it intended," it added.
Kim said that South Korea should "not make a mistake of ignoring the warning", according to the report.
South Korea has urged Pyongyang to stop acts that are unhelpful to easing tension and said the tests posed a military threat.
The firings came less than a month after Kim held a surprise meeting with US President Donald Trump at the inter-Korean border village of Panmunjom and agreed to resume their working-level nuclear talks.
The report did not directly criticize the US or Trump in an apparent effort to keep hope for talks alive but could have been meant to send a message to Washington as well.
Calling Seoul's introduction of new weapons and military exercises a "suicidal act", the North Korean leader urged South Korean President Moon Jae-in to "come back to the proper stand as in April and September last year" when they held summits.
The KCNA did not elaborate, but the report was apparently referring to the joint military exercise between South Korea and the US slated for August, and Seoul's plan to bring in stealth fighter jets from Washington for deployment through 2021.
North Korea has slammed South Korea over the plan to introduce the fighters, claiming it is intended to invade Pyongyang and constitutes a violation of the inter-Korean agreement to reduce tensions.
( With inputs from IANS )