North Korea's ruling Workers' Party newspaper Rodong Sinmun on Monday reported that Kim inspected an East Sea Fleet flotilla, but did not say when the event took place.
Images showed the apparent missile test from the ship, with a person believed to be Kim, watching from another vessel.
The newspaper quoted Kim as saying the naval units should "steadily increase the capability for actual war so that they can actively carry out their combat missions" under unfavorable circumstances.
US, South Korea holding military drills
Observers believe the newspaper's report is a response to regular US-South Korea joint military drills that began on Monday.
US and South Korean military officials say the drills are meant to prepare for emergencies on the Korean Peninsula as Pyongyang ramps up its nuclear and ballistic missile programs. The exercises – Ulchi Freedom Shield – will play out through the end of the month.
The officials also cite the shifting security environment following Russia's invasion of Ukraine.
South Korea's Yonhap News Agency has quoted a high-ranking military official as saying the drills will involve about 30 field training events. That's more than double the number carried out last year.
South Korea's military plays down North's announcement
South Korea's Joint Chiefs of Staff dismissed North Korea's claims of a strategic cruise missile test as exaggerated. It said Monday's announcement contained "many factually inaccurate aspects," but did not elaborate.
In a separate briefing, a South Korean military official explained that it would not make sense to launch strategic missiles that can carry nuclear warheads from a small ship.
The official went on to say that the weapon referred to is believed to be an anti-ship missile used to attack an enemy ship from a vessel.
The official added that the ships that launched the missiles were not built within the past 10 years, describing them as conventional and not new.
North's strategic cruise missile tests
North Korea is believed to be testing strategic cruise missiles designed to carry tactical nuclear warheads with a range of 1,500 to 2,000 kilometers – and appears to be launching them on a regular basis.
Experts believe these cruise missiles are highly accurate. The missiles are also thought to be difficult to intercept because they fly at low altitudes in elliptical or figure-eight trajectories for long periods of time.
In February this year, the military's strategic cruise missile unit fired four strategic cruise missiles from a mobile launcher into the Sea of Japan. They say the missile flew a total distance of 2,000 kilometers, taking more than 2 hours and 50 minutes before hitting a target.
The following month, two strategic cruise missiles were launched from a submarine in the Sea of Japan. This took place one day before the US and South Korea began joint military drills.
Ten days later, during the military exercise, North Korea again announced the launch of four strategic cruise missiles toward the Sea of Japan. They said that the missiles flew for up to two and a half hours, travelling 1,500 to 1,800 kilometers, before hitting targets at sea.
North Korea pledged to develop medium- and long-range cruise missiles in its 5-year national defense program revealed in January 2021.