“Why would Kim Jong-un insult me by calling me ‘old’ when I would NEVER call him ‘short and fat’?” he wrote.
“Oh well, I try so hard to be his friend – and maybe someday that will happen!”
Mr Trump made the comment after attending the Asia-Pacific Economic Cooperation (Apec) summit in Danang.
Speaking later in Vietnam’s capital, Hanoi, the US President said it “would be very, very nice” if he and Mr Kim could become friends.
“That might be a strange thing to happen, but it’s a possibility,” he said.
North Korea’s state media agency KCNA had accused the US President of escalating tensions between the two countries “to the extremes” and called on America to “oust” its leader.
“No-one can predict when that lunatic old man of the White House, lost to sense, will start a nuclear war,” KCNA had said. “The world is undergoing unprecedented throes because of Trump, a notorious ‘political heretic’.”
“The US must oust the lunatic old man from power and withdraw the hostile policy towards the DPRK at once in order to get rid of the abyss of doom.
“The US had better make a decisive choice ... if it does not want a horrible nuclear disaster and tragic doom.”
The KCNA's calls for Mr Trump's removal come after the billionaire attacked the “haters and fools” who he said are preventing the development of good relations forming between the US and Russia.
“When will all the haters and fools out there realise that having a good relationship with Russia is a good thing, not a bad thing,” Mr Trump tweeted.
The President came under fire after making remarks on Saturday that suggested he believed Russian leader Vladimir Putin’s assertions that his country had not meddled in the election that took Mr Trump to the White House.
The comments drew criticism as US intelligence agencies had already concluded there had been Russian meddling in the election race.
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