North Korean leader Kim Jong Un, right, looks at the monitors as a test launch of a missile on Jan. 11, 2022 in North Korea. AP
Pictures in state media showed Kim using binoculars to observe the second missile launch by the nuclear-armed nation in less than a week.
Hypersonic missiles are listed among the "top priority" tasks for strategic weapons development in North Korea's five-year plan.
After the launch, Kim said North Korea must "further accelerate the efforts to steadily build up the country's strategic military muscle both in quality and quantity and further modernize the army", according to KCNA.
The Tuesday test, which came as the UN Security Council met in New York to discuss Pyongyang's weapons programme, sparked swift condemnation, with the US State Department branding it a "threat... to the international community."
It was the third reported North Korean test of a hypersonic gliding missile. The first, which took place four months ago, was followed by one last week.
North Korea's state news agency KCNA said the most recent test demonstrated "the superior manoeuverability of the hypersonic glide vehicle". It also claimed it accurately hit a target some 1,000 kilometers (620 miles) away.
South Korea's military, which had cast doubt on Pyongyang's initial claims, said the missile launched on Tuesday had reached hypersonic speeds and showed clear signs of "progress" from last week's test.
The missile flew 700 kilometres (435 miles) at an altitude of about 60 kilometres (37 miles) at Mach 10 speed, Seoul's Joint Chiefs of Staff said.
Hypersonic missiles travel at speeds of at least Mach 5 -- five times the speed of sound -- and can manoeuvre mid-flight, making them harder to track and intercept.
"Everything about this test is a reminder that North Korea is all-in on a new military modernization campaign," Ankit Panda of the Carnegie Endowment for International Peace said on Twitter Wednesday.
"Kim's working his way down his 8th Party Congress wish list and is once again personally guiding tests," Panda said, referring to a recent meeting of high-level North Korean officials.
Russia, the United States and China have all reported successfully testing hypersonic glide missiles. Russia is generally seen as the world leader in the technology.
Leif-Eric Easley, a professor at Ewha University in Seoul, said the weapon was not ready for deployment.
"Nonetheless, Pyongyang's ability to threaten its neighbours continues to grow," he said.
The fact that Kim attended the missile test indicates that North Korea is satisfied with the level of progress, said Lim Eul-chul, a professor of North Korean studies at Kyungnam University in Seoul.
"Since ... the test was the final verification, additional tests of hypersonic missiles, at least, are not expected for a while," Lim said.
The tests come as North Korea has refused to respond to US appeals for talks.
At a key meeting last month of North Korea's ruling party, Kim vowed to continue building up the country's defence capabilities, without mentioning the United States.
Dialogue between Washington and Pyongyang remains stalled, and the country is under multiple sets of international sanctions over its nuclear and ballistic missile programmes.
The impoverished nation has also been under a rigid self-imposed coronavirus blockade that has hammered its economy.