The report comes amid signs North Korea could soon resume nuclear testing according to South Korean and US officials and after Kim broke a self-imposed moratorium on intercontinental ballistic missile (ICBM) testing with a launch last month.
South Korea's military said on Sunday it had detected late on Saturday two projectiles launched from the North's east coast towards the sea which flew about 110 kilometres with an apogee of 25 kilometres and maximum speed of under Mach 4.
"The new-type tactical guided weapon system ... is of great significance in drastically improving the firepower of the frontline long-range artillery units and enhancing the efficiency in the operation of tactical nukes," KCNA said.
KCNA did not say when the test took place and gave no details of the missile involved.
Upon guiding the test, Kim "gave important instructions on further building up the defence capabilities and nuclear combat forces of the country," the KCNA said.
Ankit Panda, a senior fellow at the US-based Carnegie Endowment for International Peace, said the weapon was likely a short-range ballistic missile and the North's first tactical nuclear weapon delivery system.
One reason for the timing could be to protest anticipated joint US-South Korea military drills.
On Saturday, the US 2nd Infantry Division, based in South Korea, shared photos of troops test firing a multiple launch rocket system, though it was unclear when the drills took place.
The live-fire exercises were to "ensure we maintain our readiness here in support of the ROK-US Alliance," the division said on Twitter, using the initials of South Korea's official name.
US Special Representative Sung Kim is due in Seoul on Monday for a five-day visit to discuss a response to the North's recent missile launches with his South Korean counterparts.
The United States has said it is open to talks with North Korea at any time and without preconditions, but Pyongyang has so far rebuffed those overtures, accusing Washington of maintaining hostile policies such as sanctions and military drills.
The KCNA report also came shortly after North Korea celebrated on Friday the 110th anniversary of the birth of late founder Kim Il Sung, one of the biggest annual public holidays in the country, but without a military parade.
