Kim accused Trump of exhibiting "mentally deranged behavior" and threatened him with a harsh response.
However, North Korea tested another missile on September 15 in response to the latest set of sanctions imposed by the UN.
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 USA mainland.
Previous earthquakes in North Korea have indicated nuclear tests by the nation, which is at loggerheads with the U.S. and the rest of the global community over its weapon development.
Trump responded with a tweet calling Kim Jong-un "a madman" who "will be tested like never before!" President Trump stated that the world leaders should support his decision to isolate the DPRK, as its leader is obsessed with nuclear weapons and is reckless.
The U.S. Geological Survey and Japan's Meteorological Agency both detected the tremor but said they could not judge the cause.
The most recent exchange of expletives began when Trump addressed the United Nations General Assembly for the first time on Tuesday.
Just hours before Ri took the United Nations podium, USA bombers flew off the east coast of North Korea, flying the furthest north of the demilitarized zone of any U.S. aircraft this century.
The test sparked the latest raft of United Nations sanctions and has raised tensions between the USA and its allies and the North Korean regime. "The order enhances the treasury department's authorities to target any individual or entity that conducts significant trade in goods, services, or technology with North Korea". "That's something to take seriously alone", he said.
"The quake is presumed to have occurred naturally, a sound wave, which is usually generated in the event of an artificial natural disaster, was not detected, " said an agency official.
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