On Tuesday morning local time, North Korea launched an intermediate-range missile that flew over Japan before landing in the Pacific Ocean 733 miles east of Cape Erimo, the southernmost point on Hokkaido Island, according to the Japanese government.
The South Korean military said the missile, known in North Korea as a Hwasong-12, flew 1,667 miles horizontally and about 310 miles at its top altitude after being launched.
Kim was present to observe the drill, KCNA reported, and photos were released that purport to show the leader watching the test.
"He learned in detail about the launch plan, preset flight track and target waters and issued an order to launch the rocket," according to KCNA.
According to KCNA, the missile was launched "as a part of the muscle-flexing to counter" ongoing joint U.S.-South Korean military drills.
KCNA reported that Kim expressed "great satisfaction over the successful launching."
On Friday, North Korea fired three short-range missiles that landed in the Sea of Japan, two of them traveling about 150 miles and one failing in flight. U.S. officials identified those missiles as short-range Scud missiles.
North Korea's biggest achievements so far were the country's successful launches of intercontinental ballistic missiles (ICBM) in July proving they could reach the continental United States.
On Aug. 8, Trump threatened North Korea with "fire and fury like the world has never seen," touching off a war of words between the two governments.
Kim said he would consider sending missiles into the waters off the coast of Guam in "mid-August." Guam is a U.S. island territory that is home to two American military bases.
But, after reviewing those plans, Kim ultimately decided he would “watch a little more the foolish and stupid conduct of the Yankees," seeming at the time to walk back an imminent threat to the island and de-escalating tensions on the Peninsula.
Following this week's launch, Trump warned that "all options are on the table" as the United States considers its response.
"The world has received North Korea's latest message loud and clear: This regime has signaled its contempt for its neighbors, for all members of the United Nations and for minimum standards of acceptable international behavior," said Trump in a statement Tuesday.
"Threatening and destabilizing actions only increase the North Korean regime's isolation in the region and among all nations of the world," he added.
ABC News' Adam Kelsey contributed to this report.