Pyongyang accuses Washington and Seoul of the assassination in Malaysia in order to tarnish the North’s image.
Trump made the comments to reporters as he departed his Mar-a-Lago resort in Florida, where he spent the weekend. Trump said administration officials had meetings over the weekend about North Korea, among other issues.
“Had meetings on North Korea. He’s acting very, very badly. I will tell you, he’s acting very badly,” Trump said.
North Korean state media said Kim oversaw a powerful new rocket engine test at the Sohae Satellite Launching Ground.
“He emphasised that the whole world will soon witness what eventful significance the great victory won today carries,” Pyongyang’s KCNA news agency said.
Kim said earlier this year that the millitary was preparing to test an intercontinental ballistic missile.
US Secretary of State Rex Tillerson was in China over the weekend on the last stop of a three-nation tour of Northeast Asia.
North Korea has dominated Tillerson’s agenda, with Washington seeking new ways to scupper Pyongyang’s nuclear ambitions. Previous efforts, including talks and sanctions, have failed.