Kim did not elaborate other than to say his future actions would be "beyond" Trump's expectation.
The rhetorical battle came as outside experts say North Korea is getting closer to achieve its long-stated goal of building nuclear-armed missiles capable of hitting anywhere on the United States mainland.
He ended by saying he would "surely and definitely tame the mentally deranged U.S. dotard with fire".
North Korean leader Kim Jong Un (not pictured) guides the launch of a Hwasong-12 missile in this undated photo released by North Korea's Korean Central News Agency (KCNA) on September 16, 2017.
The US government, as well as the United Nations, is still waiting for China, the benefactor of North Korea, to accept the sanctions and to join in the control measures imposed on the regime, hoping that the conflict will not get out of hand.
Earlier this month, North Korea conducted its sixth and most powerful nuclear test to date and fired a ballistic missile over Japan.
He said Kim had a tendency to "dismiss with a smirk" outside efforts to rein in the North's nuclear and missile programs, and cited the North's history of "deceiving us and buying time".
The statement, which called Trump "a frightened dog" and a "dotard", was delivered by Kim Jong Un himself, and even included a picture of the North Korean leader sitting behind a desk, apparently reading from the statement.
The new U.S. order will allow Treasury Secretary Steven Mnuchin to blacklist foreign banks that conduct or facilitate significant transactions tied to North Korean trade or with those under existing sanctions.
"There is a need to avoid any action that will interfere with the pressure being applied on North Korea", an official quoted Abe as saying at the meeting.
"Foreign financial institutions are now on notice that going forward they can choose to do business with the United States or North Korea but not both", Mnuchin told reporters.
"No matter the changes in circumstance, no matter how long it takes, not matter the difficulties we face, China will always persist in the goal of denuclearising the peninsula, in moving towards talks", he said.
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