They also argue against doing anything that might hurt ordinary North Koreans.
"I will make the man holding the prerogative of the supreme command in the US pay dearly for his speech calling for totally destroying [North Korea]", Kim said.
The trial of two women, an Indonesian and a Vietnamese, charged for the murder of Kim, is set to begin in Kuala Lumpur on Oct.2, but the North Koreans sought by police were believed to have fled Malaysia soon after the murder. That was before the arrival of Trump.
Moscow and Beijing have proposed kick-starting negotiations with North Korea by freezing Pyongyang's nuclear and missile tests in exchange for a suspension of South Korean-US annual military drills.
Kim's statement also seems to signal more weapons tests on the horizon - a worrying prospect given the North's willingness to back up its belligerent rhetoric against Trump with action.
Pyongyang conducted its sixth and largest nuclear test on September 3 and has launched dozens of missiles this year as it accelerates a program aimed at enabling it to target the United States with a nuclear-tipped missile.
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Kim said he is "thinking hard" about his response and that he would "tame the mentally deranged U".
North Korean officials described Trump's speech as "the most outrageous declaration of war against our republic, " and said Trump's statements is "priming powder" that is setting "tens of millions civilians in ultra-response mode".
North Korean Foreign Minister Ri Yong-ho, who is now visiting NY, later said the action might be the testing of a hydrogen bomb in the Pacific Ocean.
North Korea's foreign minister seemed to confirm this on the sidelines of a global United Nations meeting in NY, telling reporters that Kim's comments could mean that North Korea will conduct an H-bomb test in the Pacific, according to South Korea's Yonhap news agency. It would also be seen as extraordinarily provocative by Washington, significantly raising the chances of USA retaliation. In a one-and-only such test in 1962, the USA launched a nuclear-tipped ballistic missile from a submerged submarine. "It is truly terrifying if something goes wrong", he added.
Tensions have risen in recent weeks over North Korea's nuclear and ballistic missile tests, despite intense pressure from world powers.
China accounts for about 90 percent of North Korea's trade, making its cooperation critical to any efforts to derail Pyongyang's development of nuclear weapons and long-range missiles. It has, after all, for decades made the state-backed issuance of intimidation a crucial part of its interaction with the outside world.
The comments followed an early morning tweet from Trump, in which he called the North Korean leader a "madman" and said he "would be tested like never before".
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