Bizarrely, the first secretary of the North Korean embassy in Rome sent Italian senator Antonio Razzi the letter at a time when tensions are high on the Korean peninsula following Kim firing six ballistic missiles.
Mr Razzi criticised both leaders for “not looking into each other’s eyes” as they wage a war on words against each other.
The letter said: “The speech made by the US President in his maiden address in the UN arena in the prevailing serious circumstances, in which the situation on the Korean peninsula has been rendered tense as never before and is inching closer to a touch-and-go state, is arousing worldwide concern.”
President Trump threatened to “totally destroy” North Korea in his UN speech and he called on “righteous” countries to confront the nation.
In the speech. he said: “If the righteous many do not confront the wicked few, then evil will triumph.”
The leader of North Korea said in the letter: “Shaping the general idea of what he would say, I expected he would make stereo-typed, prepared remarks a little difference from what he use to utter in his office on the spur of the moment as he had to speak on the world’s biggest official diplomatic stage.
“But far from making remarks of any persuasive power that can be viewed to be helping to defuse tension, he made unprecedented rude nonsense one has never heard from any of his predecessors.
“A frightened dog barks louder.”
The despot leader advised President Trump in the letter to be careful when he chose his words in a speech in front of the world.
He also accused the President of having “mentally deranged behaviour”.
Speaking in a video in the the Italian newspaper Il Fatto Quotidiano, Mr Razzi said: “There are accusations against Trump.
“They accuse each other without even looking into each other’s eyes.
“That’s not ok. That is why I offered myself to help dialogue, but no one listens to me.”
The Italian senator revealed recently that Kim was a Manchester United fan.
He also has said he wants to take the football striker Paulo Dybala to North Korea as “Kim Jong-un is very passionate about sports”.