The fresh round of personal insults began earlier this week when Trump dubbed Kim "Rocket Man" on Sunday and again used the moniker at the United Nations, saying Kim is "on a suicide mission for himself".
Referring to Trump's Tuesday speech at the UN General Assembly, Kim said: "A frightened dog barks louder". "I am now thinking hard about what response he could have expected when he allowed such eccentric words to trip off his tongue", he added.
North Korea has previously said it is planning to strike the US Pacific territory of Guam.
"The United States has great strength and patience", Trump said, "but if it is forced to defend itself or its allies, we will have no choice but to totally destroy North Korea". Without explicitly naming Trump or Kim, Russian Foreign Minister Sergei Lavrov said, according to news agency Reuters, "We have to calm down the hot heads".
Mr Trump signed an executive order on Thursday to introduce fresh sanctions on Pyongyang over its nuclear weapon programme.
The US president's move to punish foreign companies that deal with the North was the latest salvo in a US-led campaign to isolate and impoverish Kim's government until his country halts its missile and nuclear tests. "This could probably mean the strongest hydrogen bomb test in the Pacific Ocean".
A commentary from the North's official Korean Central News Agency on Friday accused the party newspaper People's Daily and other party news outlets of "kowtowing to the ignorant acts of the Trump Administration".
He said the US' goal is "complete denuclearisation" of North Korea. Oh, and Trump might have finally pissed him off to the point of nuclear war.
After all, the North Korean ambassador left even before the US President began his speech.
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