Tensions over the North's weapons programmes have mounted this year and it carried out two ICBM tests last month, overseen by Kim, that apparently brought most of the United States within range.
A series of threats followed from both sides, and while the rhetoric has since eased, the US and South Korea this week kicked off their annual Ulchi Freedom Guardian military drills, which the North always condemns as dress rehearsals for invasion.
Earlier this week the official Korean Central News Agency (KCNA) described President Donald Trump as a "mad guy" in a commentary, referring to "the master of the White House who frequently posts weird articles of his ego-driven thoughts in his twitter and spouts rubbish to make his assistants have a hard time".
Kim inspected the Chemical Material Institute of the Academy of Defence Science, which develops the North's missiles, KCNA reported Wednesday.
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"He instructed the institute to produce more solid-fuel rocket engines and rocket warhead tips," it said.
Questions remain whether the North has mastered the technology needed to ensure a ballistic missile warhead survives the intense heat generated by re-entering the Earth's atmosphere, although it says it has done so.
The manufacturing process included carbon fibre weaving, chemical deposition and high pressure liquid deposition, KCNA said.
The North has threatened to fire a salvo of missiles toward the US Pacific territory of Guam, but has since backed away from the plan.
US Secretary of State Rex Tillerson on Tuesday added momentum to tension reduction, praising the North for showing a "level of restraint" in not conducting nuclear or missile tests since new UN sanctions were imposed.
He also expressed hope that it was a sign of Pyongyang's readiness to enter peace and disarmament talks with Washington "sometime in the near future."
