Regarding relations with the US, Kim said he was ready to meet with US President Donald Trump again at any time, but warned he would "find a new path" if the US were to test North Koreans' patience with sanctions and pressure.
Kim called his June summit meeting with Trump "instructive" and said they had shared "constructive opinions" on mutual concerns and "speedy solutions to the tangled issues" they faced.
Kim's speech "expressed his frustration with the lack of progress in negotiations so far", said former South Korean vice unification minister Kim Hyung-seok.
The US special representative for North Korea, Stephen Biegun, reiterated last month that Washington had no intention of easing sanctions but had agreed to help South Korea send flu medication to North Korea, saying such cooperation could help advance nuclear diplomacy.
Kim's speech comes after year of diplomatic surprises by the reclusive leader, including an unprecedented summit with Trump and three meetings with Moon. Trump's national security adviser John Bolton has said the meeting could take place in January or February.
Mr Kim's ability to carry out his threats appeared limited if Mr Trump maintains his hard line.
North Korea did not conduct any weapons tests in 2018. Over the past year, the North destroyed a nuclear testing site in Punggye-ri in the presence of global reporters, returned the remains of USA soldiers killed during the 1950-53 Korean War and released detained United States citizens.
Clad in a suit and tie and sitting on a plush armchair, Mr Kim said bilateral ties would propel ahead if the United States were to "respond by taking trustworthy and corresponding, practical action".
And it has been this immediate issue, rather than the long-term question about American troops, that bogged down negotiators from both countries towards the end of a year ago.
In this file photo taken on June 11, 2018 North Korea's leader Kim Jong Un, right, walks with US President Donald Trump, left, during a break in talks at their historic US-North Korea summit, at the Capella Hotel on Sentosa island in Singapore.
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North Korea also has bristled at USA demands to provide a detailed account of nuclear and missile facilities that would be inspected and dismantled under a potential deal.
He also emphasized a strong willingness to meet Moon frequently in 2019 as well to move forward discussion on peace and prosperity.
Kim has previously said he would close the Yongbyon nuclear facility, where North Korea is believed to produce fissile material for nuclear weapons, if Washington takes what it calls "corresponding measures".
Kim said he wanted to restart a joint economic zone in Kaesong and a joint tourism project at Mount Kumgang in the North "without preconditions".
Although the North did not conduct nuclear or missile tests a year ago, satellite images and leaked information from intelligence officials have pointed to ongoing activity at facilities in the secretive country.
Kim emphasized that it is his firm intention to work on building "new relations" with the US, establishing lasting peace on the Korean Peninsula and seeking "complete denuclearization", as agreed to in his June summit with Trump, if the USA takes trustworthy and corresponding measures.
He also called for an end to joint military drills between the US and South Korea and said no strategic military assets should be brought onto the Korean peninsula.
Joshua Pollack, a senior research associate at the Middlebury Institute of International Studies at Monterey, California, tweeted that nothing had changed in North Korea's position. Some analysts say North Korea has been trying to drive a wedge between Washington and Seoul while putting the larger burden of action on the United States.
Some experts say it's becoming clear the North intends to keep a nuclear arsenal and turn the talks with the United States into a bilateral arms reduction negotiation between two nuclear states, rather than a unilateral process of surrendering its arsenal.