The tests on Thursday to improve weapons capabilities are required because of the grave threat posed by outside forces to the security of the country, Kim, who led the tests, was quoted as saying.
The account followed the firing of multiple short-range ballistic missiles on Wednesday reported by the South Korean military, which was the second time the North test-launched missiles in a week.
Last week, North Korea also unveiled a uranium enrichment facility, in its first such public report.
Kim stressed "the need to continue to bolster up the nuclear force and have the strongest military technical capability and overwhelming offensive capability in the field of conventional weapons too," KCNA said.
Wednesday's tests involved the new tactical ballistic Hwasongpho-11-Da-4.5 missiles, KCNA said, indicating it was part of a series of short-range ballistic missiles it had been developing.
The missile was mounted with a 4.5-ton super-large conventional warhead, KCNA said.
North Korea's state media reported the tests of missiles with the same name in July, which was considered a partial success. On Thursday, state media released photographs of a projectile striking a target in a hilly area.
South Korea's military on Thursday said two ballistic missiles landed in a mountainous area in the North's northeast.
Such a missile launch test with an intention to hit an inland target is likely unprecedented, said Shin Seung-ki who is the head of research on North Korea's military at the state-run Korea Institute for Defense Analyses in Seoul.
North Korea routinely test-launches missiles to drop in the sea or on an uninhabited island.
