In his New Year's address on North Korean state television, Kim said that he was anxious to meet with President Trump at any time and that he desired to forge an agreement that would be "welcomed by the worldwide community", according to NPR.
Kim also called for South Korea to "completely stop" joint military drills with the United States involving strategic assets, while multilateral negotiations should be pursued to build a permanent peace regime on the Korean Peninsula. These are the Gaeseong industrial park in North Korea, where South Korean factories use North Korean labor, and the Mount Geumgang resort in North Korea.
Neither of those are now possible for South Korea unless sanctions on the North are removed.
There was no immediate comment from the White House and asked for a reaction, a spokesperson for the U.S. State Department said: "We decline the opportunity to comment."Washington and Pyongyang appear to have interpreted what exactly this means differently.
Kim made clear in his speech that he's ready to meet with President Trump for another summit. In exchange, the United States would have to offer major inducements, including sanctions relief.
To that end, Kim used his New Year's address to call for a permanent end to joint military drills between the USA and South Korea.
The North has dismantled some testing facilities but there are allegations it is continuing its weapons programme.
Following the June summit, reports based on satellite imagery suggested that North Korea was continuing or expanding its ballistic missile production.
"Over the past year, signs of continued work on the arsenal were alarming but not duplicitous, because there was never a commitment to stop those activities", Mount said.
The two leaders traded personal insults - Trump mocked Kim as "Little Rocket Man", who in turn called him a "mentally deranged U.S. dotard" - and threats of war as fears of conflict rose.
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Their year-end tally has only ever been bettered twice, by Chelsea (55) in 2005/06 and Manchester City (58) last season. Maurizio Sarri's side tightened their grip on the Champions League places after Arsenal lost at Liverpool .
Duyeon Kim, from the Center for a New American Security, told CNN that the New Year's message was "confident" and "normal", but added that the message to the USA was clear: "He still sent a very firm word of caution, bordering a nuanced threat, that if Washington doesn't keep its Singapore promise and continues with sanctions, then he has Plan B in mind and will go his separate way".
In his address, Kim also conveyed greetings to South Korean people, noting the trend toward reconciliation, which resulted from his meetings with Moon in 2018.
Kim's speech comes after year of diplomatic surprises by the reclusive leader, including an unprecedented summit with Trump and three meetings with Moon.
The New Year speech is a key fixture in the North Korean political calander, setting the agenda for the year to come.
Mr Kim also met with President Moon three times last year - twice at the border truce village of Panmunjom and once in the North's capital Pyongyang - and at the weekend vowed to meet Moon "frequently" this year.
Nuclear talks between Washington and Pyongyang have stalled since then, and Mr Kim's New Year address has cast further doubt on whether he is willing to give up the weapons after all.
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. -North Korea denuclearization talks remain at an impasse months after a landmark June summit between Kim and Trump in Singapore.
While the North has stopped missile and nuclear testing, there's been little indication that Pyongyang is working towards complete and verifiable denuclearisation as the U.S. has called upon it to do.
Washington and Pyongyang have yet to reschedule a meeting between U.S. Secretary of State Mike Pompeo and senior North Korean officials after the North canceled it at the last minute in November.
It is thought the North Koreans will push for a quick second summit, as they like their chances of winning concessions from Mr Trump that they might not get from lower-level officials.