Kim was shown in state media images surrounded by uniformed generals inspecting a row of compact green warheads identified as the "Hwasan-31", which means volcano in Korean.
The North has long sought the technology to "miniaturise" a nuclear warhead allowing it to be mounted on its intercontinental ballistic missiles to threaten the United States. Diagrams on the walls in the photos indicate this could be possible with the Hwasan-31.
Kim was briefed by officials from the North Korean nuclear weapons institute, the official Korean Central News Agency (KCNA) reported. He called on them to expand "the production of weapon-grade nuclear materials" for an "exponential" increase in the North's arsenal.
Kim also "put spurs to continuing to produce powerful nuclear weapons" that he said would strike fear into the North's enemies, KCNA said.
Experts warned the unveiling of a potential tactical nuclear weapon did indeed show key signs of technical progress, and could indicate an imminent nuclear test.
It came as a US Navy carrier strike group arrived in South Korea on Tuesday.
Relations between the two Koreas are at one of their lowest points in years, with Seoul and Washington ramping up joint military drills as North Korea conducts ever more provocative weapons tests while blaming the South for the deteriorating security situation.
"The current hard-line approach is likely aimed at justifying their tests for new weapons and a nuclear test in the future," said Cheong Seong-chang, a researcher at the Sejong Institute.
"North Korea unveiled a significantly miniaturised tactical nuclear warhead this time," he said.
"The possibility that North Korea will carry out a seventh nuclear test with these tactical nuclear warheads as a next step has increased," Cheong told AFP.
Too expensive?
Pyongyang has got into a pattern of "tit-for-tat" missile launches and tests to counter US and South Korean military exercises, which represents a huge -- and unsustainable -- financial outlay for the impoverished country, one expert said.
"North Korea warned of an overwhelming response against each South Korea-US joint training, but looking at the number of missiles fired, they can't continue this forever," Park Won-gon, a professor at Ewha University in Seoul, told AFP.
"If so, the seventh nuclear test will mark some kind of an end, they will declare themselves a nuclear power, and they will turn to negotiating with the United States," he said.
The North Korean military also conducted a firing drill on Monday, simulating a nuclear attack using tactical ballistic missiles, KCNA said in a separate report, part of a record-breaking streak of tests over the past year.
"North Korea is sending a very coherent message. They are fighting for recognition as a perfect nuclear power," Park said.
Underwater drone?
North Korea is seeking to diversify its delivery mechanisms in addition to increasing its nuclear stockpile.
It claimed on Tuesday to have conducted a second successful test of a new underwater nuclear attack drone.
The first test of the Haeil, which means tsunami in Korean, was claimed to have been carried out last week in what Pyongyang said was a response to recent US-South Korea military exercises, the largest in five years.
Seoul has cast doubt on the claim, with the South's military saying it was "weighing the possibility" the test had been exaggerated or even "fabricated".
There were some indications "North Korea is developing unmanned submarines, but it is evaluated that they are still in the early stages", the Joint Chiefs of Staff said.
Pyongyang said on Tuesday the Haeil had manoeuvred underwater "for 41 hours and 27 minutes tracking a simulated route spanning 600 kilometres" before destroying a target off North Hamgyong province early Monday, according to another KCNA report.
The test "proved all strategic qualifications as well as safety and reliability in the weapons system", KCNA said.
Russia has also reportedly developed a similar weapon, the nuclear-capable Poseidon torpedo, but mastering the complex technology required for such weaponry might yet be beyond North Korea, experts have said.