North Korea leader Kim Jong Un and US President Donald Trump shake hands during their first meeting in Singapore in June 2018.
"I am willing to sit with the U.S. president any time in the future and will strive to produce outcomes that would be welcomed by the worldwide community", Kim said, wearing a suit and tie and seated in a plush leather chair overlooked by paintings of his father and grandfather at work.
Kim met US President Donald Trump to discuss denuclearisation in June 2018 but with few results so far.
Kim also said the US should continue its halt to joint military exercises with South Korea and not deploy strategic military assets to the South.
Although Pyongyang did not conduct nuclear or missile tests past year, satellite images have pointed to continued activity at the North's related facilities.
In particular, Kim urged Washington not to deploy strategic weapons to South Korea and not to conduct drills that could be aimed against Pyongyang.
In October, the president said he wanted to hold a fresh summit with Kim after the midterms, but did not specify a date.
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."
"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.
"We are willing to resume the Kaesong industrial complex and tour program to Kumgangsan without any preconditions or price, in consideration of South Korean businessmen who once worked at the complex and their hard situation, along with the hopes of our South Korean comrades who seek to visit our people's famous mountain", Kim said in his speech. At the summit, the president hailed a new beginning in U.S.
North Korean leader Kim Jong Un brought a new look to his New Year's address - ditching the formalities of a podium and microphone bank to speak from a plush leather chair in front of a wooden mantle piece.
In the 30-minute speech, Kim spent more than 20 minutes highlighting his campaign to create a "self-reliant" economy despite a "harsh economic blockade".
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.
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.
Last year's speech was seen as especially significant because it presaged North Korea's diplomatic opening in 2018, a shift to better relations with South Korea and a more positive global outlook that appears set to continue in 2019, judging from Kim's latest address.
"North Korea has always been adept at putting the onus for action on the United States, taking the initiative in a way that forces Washington to either react on Pyongyang's terms or look like the obstacle to progress", Mintaro Oba, a former USA diplomat specialising in the Koreas, told the Telegraph.
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 USA has called upon it to do.
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 USA officials in its negotiations. 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.