Kim expressed "great satisfaction" with the tests, which he said showed the country's nuclear combat forces were at "full preparedness for actual war" and sent a "clear warning to the enemies," KCNA said.
With talks long stalled, and Ukraine-linked gridlock at the United Nations stymying the chance of fresh sanctions, Kim has doubled down on developing and testing his banned nuclear arsenal.
Officials in Seoul and Washington have been warning for months that Pyongyang is ready to conduct another nuclear test -- which would be the country's seventh.
Kim said North Korea will "focus all efforts on the endless and accelerating development of the national nuclear combat armed forces," KCNA reported Thursday.
Pyongyang is not technically banned by the UN from testing cruise missiles, but all ballistic missile launches violate sanctions and are typically flagged by Seoul or Tokyo. Neither had alerted the Wednesday test.
Kim made acquiring tactical nukes -- smaller, lighter weapons designed for battlefield use -- a top priority at a key party congress in January 2021.
"The latest test means the North is operating tactical nuclear capability on cruise missiles, which are harder to detect for their low-altitude flight," Hong Min of the Korea Institute for National Unification told AFP.
"It is a testament to Pyongyang's capability to mount nuclear warheads," he said, adding that cruise missiles can also have irregular flight paths making them harder to intercept.
North Korea revised its nuclear laws last month to allow preemptive strikes, with Kim declaring North Korea an "irreversible" nuclear power -- effectively ending the possibility of negotiations over its arsenal.
Since then, Seoul, Tokyo and Washington have ramped up combined military exercises, including deploying a nuclear-powered US aircraft carrier to the area twice, infuriating Pyongyang, which sees such drills as rehearsals for invasion.
In response, North Korea organised drills that it said earlier this week had gamed out hitting South Korea's ports, airports and military command facilities with tactical nukes.
North Korea has tested "strategic" cruise missiles before but this is the first time it has said they have a nuclear role and are operational -- although analysts question Pyongyang's claims, saying it has not shown it can actually make nuclear warheads small enough.
"North Korea's cruise missiles, air force, and tactical nuclear devices are probably much less capable than propaganda suggests," said Leif-Eric Easley, a professor at Ewha University in Seoul.
"The Kim regime is sometimes surprisingly transparent about weapons development goals, but it also tends to exaggerate strength and capabilities," he added.