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.
Experts here said North Korea has started preparing for a policy change in case its nuclear talks with the United States fail to move forward without the concessions it wants, such as security guarantees and the lifting of sanctions imposed over the regime's nuclear program.
What happens in the coming weeks will likely determine if Washington's next so-called "Christmas gift" turns out to be similarly volatile.
Trump mentioned on Tuesday he nonetheless had confidence within the North Korean chief however famous that Kim "likes sending rockets up".
The lack of courtesy shown to Kim had "prompted the waves of hatred of our people against the U.S. and the Americans and they are getting higher and higher", Choe said.
Negotiations between the two nations have meanwhile reached a sort of a deadlock.
Washington, for its part, has not voiced increased alarm over the status of talks with North Korea.
On Thursday, North Korea threatened to resume the insults of US President Donald Trump and consider him a "dotard" if he continues to use provocative language, such as the leader as a "rocket man".
During a visit to London, Trump said on Tuesday that his relationship with Kim was "really good", but also urged him to comply with a denuclearization commitment. "I hope he lives up to the agreement, but we're going to find out", added Trump.
Trump said he was raining "fire and rage" on North Korea and mocking Kim as a "small rocket man" while Kim trumped Trump's mind and said he "would tame the mentally disturbed United States dotard".
"... That is why I name him Rocket Man", Trump instructed reporters at a North Atlantic Treaty Organisation assembly in London. This was Kim's second trip on horseback atop the mountain since October.
All-out war could erupt between USA and North Korea "at any moment" - N. Korean media Tensions between Washington and Pyongyang continue to grow as North Korean state media warn that a simmering conflict between the two nations could turn into a full-blown war at any given moment.
Putting Kim on a horse at Mount Paektu, wearing a similar coat to the one his grandfather was often seen wearing publicly, is likely meant to remind North Koreans of the Kim family's legacy of fighting imperialism, according to Michael Madden, an expert in North Korean leadership at the Stimson Foundation.
"Kim Jong Un is taking on the anti-imperialist credentials of his grandfather", added Madden.
However, it's unclear why Kim held the photo shoot at the mountain.