In 2017 the two leaders famously engaged in a war of words, with Trump calling Kim "Rocket Man" and North Korea slamming the USA president, now 73, as a "dotard".
Pak said regime leader Kim Jong-un was "displeased" with Trump's remarks and stressed that the only thing preventing physical conflict between North Korea and the U.S.is the close relationship between their leaders.
Choe says her ministry "cannot contain its displeasure" over Trump's comments.
"If he uses statements and expressions that intentionally amplify the atmosphere of confrontation at this time of crisis, we will have to diagnose that the dotard started to be senile again", she said.
Trump's comments threaten to return the two countries to the tensions of two years ago, Choe Son-hui, first vice-minister of Foreign Affairs for North Korea, said in a statement carried by state news agency KCNA.
Earlier this week, Trump told reporters in London that Kim "likes sending rockets, doesn't he?"
US President Donald Trump, who is seeking re-election next year, has repeatedly pointed to Kim's suspension of long-range missile and nuclear bomb tests as a major achievement of his engagement with North Korea.
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"If any language and expressions stoking the atmosphere of confrontation are used once again on objective at a crucial moment as now, that must really be diagnosed as the relapse of the dotage of a dotard", she said.
"One thing I would like to make clear is that the use of armed forces is not the privilege of the U.S. only", Park Jong-chon, chief of the general staff of the Korean People's Army, said in a statement.
Tensions between the United States and North Korea have heightened as the two sides exchanged threats and bellicose rhetoric of possible military actions if necessary, amid their stalled nuclear talks.
Trump also said this week that the United States is prepared to use its military against North Korea if it has to, which has also angered Pyongyang.
The North has conducted 13 multiple rocket launcher and shirt-range missile tests that were clearly aimed at South Korea, and Kim demanded that South Korea demolish "all the unsightly facilities" built by the South in the North's Mt. Kumgang resort.
The two leaders have avoided such words and developed better relations after North Korea entered nuclear negotiations with the US a year ago.
"As long as we have the revolutionary spirit of Mount Paekdu, and revolutionary spirit of self reliance, we can survive on our own and open the door for development and prosperity of our own style", Vice Premier Kim Tok-hun said in a column. He added that "That's why I call him rocket man".