The missile on Friday traveled 2,300 miles as it flew over Japan on Friday before landing in the northern Pacific Ocean. It was the country's longest-ever test flight of a ballistic missile.
The KCNA said Kim expressed great satisfaction over the launch, which he said verified the "combat efficiency and reliability" of the missile and the success of efforts to increase its power.
Photos were also released Saturday by the North Korean government of its leader Kim Jong Un watching what it says was the test launch of the Hwasong-12 missile.
Following Friday's missile launch, Secretary of State Rex Tillerson said in a statement, "These continued provocations only deepen North Korea's diplomatic and economic isolation ... United Nations Security Council resolutions, including the most recent unanimous sanctions resolution, represent the floor, not the ceiling, of the actions we should take. We call on all nations to take new measures against the Kim regime."
The launch is the 14th missile test conducted by North Korea in 2017. On September 3, North Korea said it tested a hydrogen bomb, leading to sanctions being passed against the country by the United Nations Security Council on Tuesday.