It is the first time in over a year that Pyongyang has been openly critical of Donald Trump, the BBC’s Korea correspondent Laura Bicker said.
The Oxford English Dictionary defines a dotard as “a person whose mental faculties are impaired, specifically, a person whose intellect or understanding is impaired in old age”.
Dotage, meanwhile, is defined as “having impaired intellect or understanding in old age”, or in general use as “old age”.
The two men held face-to-face talks in Singapore in June 2018, and in Vietnam in February this year, aimed at denuclearisation.
But talks have stalled since then, and despite another impromptu meeting at the demilitarised zone (DMZ) that separates North and South Korea in June, the North has restarted testing of short-range ballistic missiles.
In recent months the hostile language has also come back.
Pyongyang has set Washington an end-of-year deadline to offer it new concessions and has said it will adopt a “new way” if that does not happen.
‘War of words’
At the Nato summit in the UK on Tuesday, Mr Trump referred to North Korean leader Kim Jong-un as “rocket man”.
He also said that the US reserved the right to use military force against Pyongyang.
In a statement carried by North Korea’s state news agency, Vice Foreign Minister Choe Son-hui warned that the “war of words” from two years ago may be resuming.
“If any language and expressions stoking the atmosphere of confrontation are used once again on purpose at a crucial moment as now, that must really be diagnosed as the relapse of the dotage of a dotard.”
In 2017, the two leaders engaged in tit-for-tat arguments, with Mr Trump dubbing Mr Kim “little rocket man” and “a madman”, while Mr Kim called the US president a “mentally deranged dotard”.