During that address the North Korean dictator said he welcomed a meeting with Trump but also issued a semi-veiled threat, saying if the USA pressures or sanctions North Korea that his nation "may be left with no choice but to consider a new way to safeguard our sovereignty and interests".
"(But) we could be left with no choice but to seek a new way if the USA does not make good on its promises, misjudges our patience, while seeking to force things unilaterally and clinging to sanctions and pressure", he said. He also added he is willing to meet US President Donald Trump at any time to produce results the global community would welcome.
However, he added: "We could be left with no choice but to seek a new way if the U.S. does not make good on its promises, misjudge our patience, while seeking to force things unilaterally and clinging to..."
The fact that Kim Jong Un's renewed commitment to denuclearisation was made not just to the outside world, but to millions of ordinary North Koreans, is seen as significant.
Mr Kim and Mr Trump met for the first time in Singapore in June but, despite a great deal of hype, the resulting agreements were vague on how denuclearisation would be achieved.
In his new year speech, he called on the USA to halt its joint military exercises with South Korea and to refrain from deploying military assets in the country.
Kim has warned Washington not to test North Koreans' patience with sanctions and pressure.
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In that speech, Kim said he had a "nuclear button" on his desk with weapons capable of reaching the United States, but he also opened a path to dialogue with Seoul and expressed willingness to send a delegation to the Winter Olympics in South Korea.
In October, the president said he wanted to hold a fresh summit with Kim after the midterms, but did not specify a date.
But Kim called on Washington to take "corresponding" and "trustworthy" measures to reciprocate steps North Korea has already taken.
"Kim is hinting that if things come to worse, North Korea could go back to the economic-nuclear dual path", Cheong Seong-chang, director of unification strategic studies program at the independent Seoul-based think tank Sejong Institute, told ABC News.
In what was the first time a North Korean leader met a sitting USA president, the two signed a vaguely phrased agreement to improve ties and work towards denuclearisation.
In this January 1, 2018, file photo provided by the North Korean government, North Korean leader Kim Jong Un delivers his New Year's speech at an undisclosed place in North Korea.
Kim also emphasized the development of the North Korean economy and, without elaborating, mentioned nuclear power as part of the country's plans to boost electricity production.
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Neither of those are now possible for South Korea unless sanctions on the North are removed.
The Seoul government shut down the joint industrial complex at the North's border town of Kaesong in 2016 in retaliation for Pyongyang's nuclear and missile provocations at the time.
He spoke warmly of his three 2018 meetings with South Korean President Moon Jae-in and of the rapprochement between the two nations, but he said that progress should be consolidated by ending joint military exercises with the United States.
But nuclear talks between Washington and Pyongyang have stalled in recent months as they struggle with the sequencing of North Korea's disarmament and the removal of US-led sanctions against the North.
The hermit-kingdom despot used his New Year address to stage the intervention.
North Korea has not responded to Washington's calls for senior working-level talks to follow up on the June 12 summit, apparently preferring to engage Trump rather than other United States officials in its negotiations.
In the clip, Trump claimed his government had taken steps to improve United States relations with North Korea.
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