In response, the United States and South Korea held combined live-fire drills, including surface-to-surface missile tests involving the Army Tactical Missile System (ATACMS) of the US and the South's Hyunmoo-2 SRBM, both militaries said.
The launch, the North’s 14th round of weapons firing this year, also came six days before a new conservative South Korean president takes office for a single five-year term.
The missile tests "did not pose any threat or harm to the safety of civil aviation as well as the safety of neighbouring countries and regions, by a full consideration of civil aviation safety in advance."
Viewing the drills as a military threat, North Korea decided to stage "the simulation of an actual war” to check and improve its war deterrence and send a warning to its enemies, KCNA said.
"We agreed to further strengthen cooperation ... so that North Korea can immediately stop its illegal activities and return to denuclearisation talks," said South Korea's Cho Hyun-dong.
The launch comes after the navies of South Korea, the United States and Japan staged trilateral anti-submarine exercises on Friday for the first time in five years, and follows a visit by US Vice President Kamala Harris to the region this week.
The last time North Korea fired a missile over Japan was in 2017, at the height of a period of "fire and fury" when Pyongyang's leader Kim Jong Un traded insults with then-US president Donald Trump.
The trio also condemned North Korea's disregard of multiple UN Security Council resolutions and its deeply destabilizing implications for the region, spokesperson Ned Price said.
North Korean leader Kim Jong Un doubled-down on his nuclear arms buildup to overwhelm "hostile forces” at a key meeting where military leaders approved unspecified new operational duties for front-line army units.