"I will tell you, he's acting very badly", Trump said.
President Trump commented on leaving his weekend retreat in Florida aboard Air Force One.
The US dismisses that claim, saying it believes North Korea is working to develop nuclear warhead missiles that could reach the United States.
That could mean striking at North Korea's facilities for launching or producing ballistic missiles or its nuclear facilities.
Kim emphasized the whole world would "soon witness what eventful significance the great victory won today carries", KCNA reported.
US Secretary of State Rex Tillerson, during his recent visit to Seoul, said that "the policy of strategic patience (with North Korea) has ended". North Korea has conducted six ICBM tests since 1998, accumulating a high degree of knowhow and technology over the years.
Relations between Malaysia and North Korea have deteriorated sharply since Kim's death, with each expelling the other's ambassador.
USA aerospace expert John Schilling said the engine appeared too big for any ICBM North Korea was working on but would be a good fit for the second stage of a new space rocket it is planning to build.
"This was a comprehensive test for the first-stage rocket for an ICBM, and that is why it was unsafe", Kim Dong-yub of the Institute for Far Eastern Studies in Seoul told Reuters.
Engines used in the Long March 2 satellite launcher were later repurposed for the "development of the DF-5 ballistic missile - China's first true intercontinental range missile", according to David Wright, co-director of the Union of Concerned Scientists.
What happens to all those millions of North Koreans, many of them starving and wanting any kind of new life in the South?
Secretary of State Rex Tillerson has signaled that the USA will take a more aggressive approach to North Korea's missile and nuclear program, including possibly through pre-emptive military action. Of the North Korean rocket and missile projects that we are now aware of, the best fit for this engine would be as the second stage of the new satellite launch vehicle provisionally known as the "Unha-9".
He's warned that the United States would consider a preemptive military strike against the regime and has called on China to do more to rein in its North Korean ally.
The US and China pledged to work together to get the North to take "a different course" and move away from its weapons programmes after Mr Tillerson met his Chinese counterpart on Saturday.
Beijing has also been infuriated by the deployment of an advanced US anti-missile system in South Korea, which it says will both harm China's own security and do nothing to ease tensions.