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The state-run Korean Central News Agency in a statement said, "Trump, during his visit, laid bare his true nature as the destroyer of the world peace and stability and begged for a nuclear war on the Korean Peninsula."
Trump is in Vietnam as part of his 12-day tour of Asia, and North Korea's nuclear weapons programme has been a major talking point with his Japanese, South Korean and Chinese counterparts.
Earlier, at the outset of this tour, Trump, in an interview broadcast stated he would "certainly be open" to meeting with North Korean leader Kim Jong-un.
Pyongyang described Trump's trip as "nothing but a business trip by a warmonger to enrich the monopolies of the US defence industry."
"It is also nothing but a business trip by a warmonger to enrich the monopolies of the US defence industry by milking the moneybags from its subordinate allies," the statement added.
The statement also referred to Trump as dotard, a word the isolated nation has used on him in the past as well.
The US and North Korea have long been engaged in back-and-forth barbs over the latter's threat of a nuclear attack.
North Korea jolted major world leaders when it carried out the strongest of its six-ever nuclear tests in early September, claiming to have used a hydrogen bomb.