- North Korea's nuclear weapons test would violate United Nations sanctions
- South Korea warns North risks "self-destruction"
- Seoul says not evidence North is preparing for more tests
Such tests would be in defiant violation of United Nations sanctions that were recently strengthened with the backing of China, North Korea's chief ally.
Mr Kim made the comments as he supervised a successful simulated test of atmospheric re-entry of a ballistic missile that measured the "thermodynamic structural stability of newly developed heat-resisting materials", the North's official KCNA news agency said.
"Declaring that a nuclear warhead explosion test and a test-fire of several kinds of ballistic rockets able to carry nuclear warheads will be conducted in a short time to further enhance the reliance of nuclear attack capability, he [Mr Kim] instructed the relevant section to make prearrangement for them to the last detail," the agency said.
South Korea's Defence Ministry said there were no indications of activities at the North's nuclear test site or its long-range rocket station, but that North Korea continues to maintain readiness to conduct nuclear tests.
South Korean President Park Geun-hye said the North would lead itself to self-destruction if it did not change and continued the confrontation with the international community.
The North's report comes amid heightened tension on the Korean peninsula as South Korean and US troops stage annual military exercises that Seoul has described as the largest ever.
US, South Korea sceptical of North's nuclear claims
The North has issued belligerent statements almost daily since coming under a new UN resolution adopted this month to tighten sanctions against it after a nuclear test in January and the launch of a long-range rocket last month.
South Korea's Defence Ministry said after the North's report that it still does not believe the North has acquired missile re-entry technology, which should include the ability to guide the rocket after it re-enters the atmosphere.
What would be terrible is if the DPRK [North Korea] re-enacted Operation Frigate Bird or the fourth Chinese nuclear test and did a two-in-one.
Jeffrey Lewis, Institute of International Studies
In 1962, the United States launched a ballistic missile with a live warhead in what was known as the Frigate Bird test. China conducted a similar test in 1966.
"What would be terrible is if the DPRK [North Korea] re-enacted Operation Frigate Bird or the fourth Chinese nuclear test and did a two-in-one," said Jeffrey Lewis of the California-based Middlebury Institute of International Studies.
"For now, though, it looks like a nuclear test and several missile tests in close succession."
US and South Korean experts have said the general consensus was that North Korea had not yet successfully miniaturised a nuclear warhead to be mounted on an intercontinental ballistic missile.
More crucially, the consensus is that there have been no tests to prove it has mastered the re-entry technology needed to bring a payload back into the atmosphere.
Mr Kim said last week his country had miniaturised a nuclear warhead.
The North, which has conducted four nuclear tests, also claims that its January nuclear test was of a hydrogen bomb, although most experts said the blast was too small for it to have been from a full-fledged hydrogen bomb.
The North also says the satellites it has launched into orbit are functioning successfully, although that has not been verified independently.