"When it comes to North-South relations, we should lower the military tensions on the Korean Peninsula to create a peaceful environment," Kim said. "Both the North and the South should make efforts."
Kim said he will consider sending a delegation to the Winter Olympics Games to be held in Pyeongchang, South Korea, in February.
"North Korea's participation in the Winter Games will be a good opportunity to show unity of the people and we wish the Games will be a success. Officials from the two Koreas may urgently meet to discuss the possibility," Kim said.
Rather than encouraging U.S. measures that "threaten the security and peace of the Korean peninsula," Seoul should instead respond to overtures from the North, Kim said.
He also called for improved relations with the South, an idea mentioned in speeches more often than it is met. He said the Pyeongchang Winter Olympics in February would be a good opportunity to showcase the status of the Korean nation.
He also said the two Koreas could meet urgently to discuss the North sending a delegation.
"The Winter Olympic games that will be held soon in the South will be a good opportunity to display the status of the Korean nation and we sincerely wish that the event will be held with good results," he said.
South Korea's presidential office said it welcomed the proposal to hold talks between government officials over the issue of North Korea sending a delegation to the Olympics. The office of President Moon Jae-in said the successful hosting of the Pyeongchang Olympics would contribute to peace and harmony not only on the Korean Peninsula and in Northeast Asia, but in the entire world.
The New Year's address is an annual event in North Korea and is watched closely for indications of the direction and priorities Kim may adopt in the year ahead.
This year's speech was seen as particularly important because of the high tensions over Pyongyang's frequent missile launches and its nuclear test in 2017. The tests were the focus of fiery verbal exchanges between North Korea and President Donald Trump, who has derisively called Kim "little rocket man."
Asked by reporters to comment on Kim's speech, Trump simply said "we'll see, we'll see," as he walked into New Year's eve celebration at Mar-a-Lago, his elite resort in Florida.
The U.S. State Department did not immediately respond to a request for comment on Kim's New Year's address.
'This is reality, not a threat'
North Korea tested intercontinental ballistic missiles and conducted its sixth and most powerful nuclear test in September in defiance of international warnings and sanctions, raising fears of a new conflict on the Korean peninsula.
After testing what Pyongyang said was its most powerful intercontinental ballistic missile (ICBM), capable of delivering a warhead to anywhere in the continental United States, at the end of November, Kim declared his nuclear force complete.
He continued that theme in his New Year's address, announcing that North Korea would focus on "mass producing nuclear warheads and ballistic missiles for operational deployment" in the coming year.
This, Kim said, made it impossible for the United States to start a war against North Korea.
"The entire United States is within range of our nuclear weapons, and a nuclear button is always on my desk. This is reality, not a threat," he said, while emphasising that "these weapons will be used only if our security is threatened."
Kim's customary New Year's speech is closely watched for indications of the policy direction the unpredictable and reclusive leader is likely to pursue in the coming year.
Beyond listing military accomplishments, Kim also outlined economic gains as part of his two-pronged policy of developing his country's economy and military.
Despite increased international sanctions imposed over the weapons programme, North Korea made progress in areas like fabrics, shoes and tractors, Kim said.
While Kim is keen to declare his weapons programme a success, he is unlikely to completely end his contentious testing regime, said Scott LaFoy, a ballistic missile analyst at the website NK Pro, which monitors North Korea.
"I'm still very skeptical of the 'complete' thing they've been talking about, if only because we've seen so much activity in regards to the submarine launched ballistic missile programme," he said. "I think a slowdown [in testing] is very realistic, though."
Kim seems likely to tone down his weapons testing at least ahead of the Olympics, said Nam Sung-wook, a North Korea expert at Korea University in Seoul.
"What North Korea is most afraid of is being forgotten in the international arena," he said. "Without launching missiles and conducting a nuclear test, North Korea will be in the spotlight just by attending the Winter Olympics."
Kim also stressed North Korea's economic achievements during the speech, and noted the importance of improving the nation's standard of living.