In his speech, Mr Kim said the United States and South Korea should no longer carry out joint military exercises - which have been largely halted since the Singapore meeting - calling such drills "a source of tension".
Since the Singapore summit where Kim committed to working toward denuclearization, talks between the USA and North Korea have stalled due to their differences over the sequencing of denuclearization.
Trump has been considering a second summit with Kim to speed up the stalling denuclearization.
Harry Kazianis, director of defense studies at the Center for the National Interest: "Kim Jong Un's message to the world today is simple: Pyongyang is clearly willing to engage in dialogue while working towards denuclearization with Washington and Seoul - but on its terms". There are views that North Korea wants a quick second summit because it thinks it can win major concessions from Trump that they probably couldn't from lower level US officials, who are more adamant about the North committing to inspections and verification.
The hermit-kingdom despot used his New Year address to stage the intervention.
The two leaders traded personal insults - Trump mocked Kim as "Little Rocket Man", who in turn called him a "mentally deranged United States dotard" - and threats of war.
Still, that summary did quote Kim as urging North Koreans to effect "a revolutionary surge on all fronts of the socialist construction by regarding self-reliance as a treasured sword for prosperity".
However, Kim's statement could prove problematic if there's ongoing evidence the North's nuclear and missile facilities continue to run. USA officials have repeatedly called for the stringent enforcement of sanctions on the country until its "final, fully verified denuclearization".
In the speech, Kim hailed the results of the North's diplomatic activities in 2018, including his three meetings with South Korean President Moon Jae-in.
He also said he was ready to meet Mr Trump again at any time.
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North Korean leader Kim Jong Un has warned there will be consequences if the USA "continues to break its promises and misjudges the patience of our people".
The North has also bristled at USA demands to provide a detailed account of nuclear and missile facilities that would be inspected and dismantled under a potential deal.
"We will never tolerate outside interferences and interventions meant to block our way toward reconciliation, unity and the unification of our people, while trying to make our relations scummy to their states and interests", the North Korean leader said, adding that "significant" agreements achieved during 2018's three inter-Korean summits could be "regarded as non-aggression treaty".
The hardening stalemate has fueled doubts on whether Kim will ever voluntarily relinquish the nuclear weapons and missiles he may see as his strongest guarantee of survival.
A rapid sequence of developments followed, with athletes and a senior delegation led by his powerful sister going to the Pyeongchang Games in February, before Kim met Chinese President Xi Jinping in Beijing ahead of the Singapore summit with Trump.
But North Korea for decades has been pushing a concept of denuclearization that bears no resemblance to the American definition, with Pyongyang vowing to pursue nuclear development until the United States removes its troops and the nuclear umbrella defending South Korea and Japan.
Kim directed part of his message at neighbor South Korea, urging it to ditch joint wargames with the United States for the sake of reconciliation.
However, there was a clear warning that the country is not ready to disarm unilaterally.
Although Pyongyang did not conduct nuclear or missile tests previous year, satellite images have pointed to continued activity at the North's related facilities.