Kim said he was willing to meet the USA president at any time, mixing in conciliatory messages with his warnings of conflict to Washington and Seoul in his annual speech where he laid out policy priorities for his isolated and impoverished country.
"If the U.S. does not keep its promise made in front of the whole world", Kim said, "we may be left with no choice but to consider a new way to safeguard our sovereignty and interests".
His previous New Year's addresses had taken place in more formal settings, with Kim standing at a podium.
But for most of his 30-minute speech, he focused on North Korea's economy and said he stands ready to resume projects with South Korea and restart operations at a jointly run factory park in the border town of Kaesong.
Pyongyang has demanded Washington lift sanctions and declare an official end to the 1950-53 Korean War in response to its initial, unilateral steps toward denuclearization, including dismantling its only known nuclear testing site and a key missile engine facility.
In a jab at the South's alliance with the U.S., Kim also said Washington should continue to halt its joint military exercises with Seoul and not deploy strategic military assets to the South. Washington stopped some large-scale exercises with Seoul, although smaller drills continued.
He also called for South Korea and the United States to end joint military exercises which Kim described as "a source of tension".
He also pointed to a potential second meeting with Trump.More news: Nawaz Sharif, Pakistan ex-PM, sent back to jail for corruption
Although Pyongyang did not conduct nuclear or missile tests a year ago, satellite images have pointed to continued activity at the North's related facilities.
Although he warned he could explore a "new path", Kim's restrained tone indicates his willingness to maintain the momentum for dialogue with the U.S., experts say.
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. "So, Kim is not so much making any new commitments so much as laying the groundwork for the United States to take the blame for any lack of progress".
Last year's speech set the country on an unprecedented path of global diplomacy with South Korea and the US. Kim also urged the North Korean people to strengthen their "self-reliance", a message that echoed Chinese President Xi Jinping's similar address Monday night.Kim repeated the importance of being "frugal" multiple times when speaking about economic plans.
Kim and Trump vowed to work toward denuclearization and build "lasting and stable" peace at their landmark summit in Singapore in June, but little progress has been made since.
"Japan, a political dwarf which has come under bitter denunciation and rejection by the worldwide community for its bad habit of seeking benefits in the troubled waters, dares to challenge the strong trend of peace and stability in the region".
In a recent letter to Moon, Kim wrote that he wants to "meet often" to "resolve together the issue of denuclearizing the Korean Peninsula". "Delivering the speech from his well-appointed study with the accompanying background videos highlighting economic development was well thought out and makes Kim appear normal, rational, and someone whom the global community can embrace and with whom it can negotiate".