The announcement on North Korea state television said the "successful" Hwasong-14 missile test was overseen by Kim.
It said the projectile had reached an altitude of 2,802km and flew 933km for 39 minutes before hitting a target in the Sea of Japan.
The altitude achieved by the missile was the highest ever reached by a North Korean missile, and puts the US on notice that Pyongyang could potentially hit the US mainland.
It would enable the country to "put an end to the US nuclear war threat and blackmail" and defend the Korean peninsula, it said.
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Reacting to the development on Twitter, Trump said, "North Korea has just launched another missile. Does this guy (Kim) have anything better to do with his life?"
"Hard to believe that South Korea and Japan will put up with this much longer. Perhaps China will put a heavy move on North Korea and end this nonsense once and for all!" he tweeted.
The US has been urging China -- North Korea's closest diplomatic ally -- to pressure the Pyongyang regime to end its nuclear and ballistic missile programmes.
In Beijing, China defended its "relentless efforts" to resolve the North Korea nuclear issue.
Foreign ministry spokesman Geng Shuang told reporters that China's contribution was well recognised internationally after Trump called on China to take stern action on North Korea.
"China has made relentless efforts for the settlement of the Korean peninsula nuclear issue. China's contribution in this regard is well recognised, and its role is indispensable," Geng said.
"China opposes the DPRK breaching UN Security Council resolutions to conduct launch activities," he said.
"We hope all relevant parties can exercise restraint, avoid taking actions that may escalate tensions, and make efforts to bring the issue back to peaceful settlement through dialogue and consultation," Geng said.
According to United States Pacific Command (USPACOM), the missile was tracked for 37 minutes and landed in the Sea of Japan.
"We are working with our interagency partners on a more detailed assessment. We continue to monitor North Korea's actions closely," the PACOM said.
"US Pacific Command stands behind our iron-clad commitment to the security of our allies in the Republic of Korea and Japan," it said.
The United Nations has imposed multiple sanctions on North Korea over its nuclear and missile programmes.
That's the highest altitude ever reached by a North Korean missile, and puts the US on notice that Pyongyang could potentially hit the US mainland.
Pyongyang appears to have timed the launch for maximum political effect, giving the order to fire on the eve of the July 4 holiday in the US, just days after President Trump spoke with Japanese and Chinese leaders about the North Korea threat and before this week's G20 meeting, CNN commented.
"That range would not be enough to reach the lower 48 states or the large islands of Hawaii, but would allow it to reach all of Alaska," Wright wrote on the All Things Nuclear blog.