The missile was launched from Sunan, an area of the North Korean capital of Pyongyang, according to South Korea's Joint Chiefs of Staff.
Meanwhile, Japanese Deputy Defense Minister Makoto Oniki said the missile is estimated to have flown at a maximum altitude of about 800 kilometers over a distance of about 500 kilometers before falling into the sea outside of Japan's Exclusive Economic Zone.
Among the weaponry on show at the parade in Pyongyang was a Hwasong-17 intercontinental ballistic missile (ICBM), multiple giant rocket launchers, and a submarine-launched ballistic missile.
"True peace can be trusted and national dignity and national sovereignty can be guaranteed by the powerful self-defense force that can overcome the enemy," Kim said in a statement released by the state-run Korean Central News Agency (KCNA) after the parade.
He said his nuclear force's first mission was "to deter war," but if anyone tried to "to take away the fundamental interests of our country, our nuclear force will have no choice but to carry out its second mission." He did not elaborate on what that second mission would be.
By comparison, it conducted only four tests in 2020, and eight in 2021.
Among this year's tests was the launch of an ICBM on March 24, North Korea's first test of that weapon in more than four years.
This is a developing story.