The latest launches were personally ordered and monitored by Kim, according to the North's official KCNA news agency.
The tests were ordered and monitored by Kim Jong-Un and the range of the missiles was limited to simulate pre-emptive attacks on South Korean ports and airfields hosting USA military "hardware", the North's official KCNA news agency said.
"Kim Jong-Un expressed great satisfaction over the successful drill", the KCNA reported, which "examined the operational features of the detonating devices of the nuclear warheads mounted on the ballistic rockets at the designated altitude over the target area".
The South's military observed three North Korean projectiles travel up to 600 kilometers (373 miles) into open water east of the peninsula a day earlier - in defiance of several United Nations resolutions barring Pyongyang from developing ballistic missile technology.
The deployment of the USA missile defense system THAAD (Terminal High Altitude Area Defense) in South Korea was decided after a series of missile launches that show, according to analysts, Pyongyang progress in its efforts to develop an intercontinental missile (ICBM) capable of carrying a nuclear attack on the American continent.
The region has been on edge since North Korea announced it had successfully tested a hydrogen bomb in January, after a magnitude 5.1 seismic event was detected inside the rogue state.
"(North Korean) numbers broadcasts have been on hold for quite some time but have recently resumed, something we think is very regrettable", Jeong Joon-hee, a spokesman for South Korea's unification ministry, told a media briefing on Wednesday.
The missiles were fired a distance of hundreds of kilometres, far enough to threaten the whole of the South.
Pyongyang fired what is thought to be two short-range Scuds and the third medium-range Rodong missile on Tuesday (19 July), which, again, escalated tensions in the Korean peninsula.
It is unclear whether North Korea actually has the technology that it boasts about having.
North and South Korea are still technically at war after the 1950-53 Korean War ended in a truce, not a peace treaty, and tensions are running high.
South Korea jams most North Korean radio frequencies but Pyongyang-based Voice of Korea broadcasts on shortwave signals which can be picked up far beyond the Korean peninsula, and are hard to jam.
It has repeatedly threatened to turn Seoul and USA bases in the Pacific into a "sea of fire" and produced videos showing Washington, D.C., in flames.