"We are not dealing with a rational person," US Ambassador Nikki Haley told reporters following a closed-door meeting of the Security Council to discuss North Korea's latest missile launches.
In a reference to China, which is calling for a return to negotiations, Haley said that "if this were any other country, we would be talking about that and it wouldn't be an issue."
She described Kim, without naming him, as a "person who has not had rational acts, who is not thinking clearly."
The UN Security Council met behind closed doors to discuss next steps to address North Korea's missile launches after Pyongyang said the latest tests were for a possible strike on US bases in Japan.
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North Korea fired at least four missiles toward Japan on Monday, three of which splashed down in waters near Japan.
The US ambassador said "all the options are on the table" and did not rule out talks completely but she made clear that the onus was on North Korea to show a willingness to seek a diplomatic solution.
China, Pyongyang's main ally, earlier called on North Korea to suspend its nuclear and missile activities in exchange for the US and South Korea halting joint military exercises in South Korea.
The proposal from the Chinese foreign minister however appeared to fall flat, with Britain, France and Japan saying that North Korea must take the first step to show that it was ready to change course and abandon its military and nuclear programs.
Chinese Ambassador Liu Jieyi stressed the importance of reducing tensions on the Korean peninsula, telling reporters after the meeting that this must be done "in a negotiated way".