In his new year address, Kim said there would be faster progress on denuclearisation if the United States took corresponding action.
Mr Kim was referring to his summit with US President Donald Trump in Singapore in June, when he said he had "fruitful talks" and "exchanged constructive ideas".
North Korea however would have "no option but to explore a new path in order to protect our sovereignty" if the United States "miscalculates our people's patience, forces something upon us and pursues sanctions and pressure without keeping a promise it made in front of the world", Kim said.
The New Year speech is a key fixture in the North Korean political calander, setting the agenda for the year to come. He said he was willing to resume joint projects with the South, including reopening the Kaesong industrial park and Mount Kumgang resort, without conditions.
If precedent is any indication, the North Korean leader will go into some detail outlining, sector by sector, the country's successes so far and emphasizing what remains to be done.
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.
Last year's rapprochement came after a turbulent 2017 marked by North Korea testing missiles that could reach the U.S. mainland and an escalation in rhetoric between Pyongyang and Washington with both sides trading insults and threats of nuclear destruction.
"We will never tolerate outside interferences and interventions meant to block our way toward reconciliation, unity and the unification of our people, while trying to make our relations scummy to their states and interests", the North Korean leader said, adding that "significant" agreements achieved during 2018's three inter-Korean summits could be "regarded as non-aggression treaty".
He also said the US and South Korea should no longer carry out joint military exercises - which have been largely halted since the Singapore meeting - calling such drills "a source of tension".
Kim and Trump vowed to work toward denuclearization and build a "lasting and stable" peace regime at their landmark summit in Singapore in June, but both sides have since been struggling to make progress.
The BBC's Laura Bicker in Seoul says this could mean that North Korea is waiting for the USA to act in 2019 and unless it does, the current pause on nuclear weapons testing could be over.
Mr Kim congratulated himself on his diplomatic activities during 2018, including meetings with South Korean president Moon Jae-in and Chinese president Xi Jinping.
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.
The hardening stalemate has fuelled doubts on whether Kim will ever voluntarily relinquish the nuclear weapons and missiles he may see as his strongest guarantee of survival.
There was no immediate reaction from the US State Department, but South Korea's presidential office welcomed Kim's speech, saying it carried his "firm will" to advance relations with Seoul and Washington.
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 cancelled it at the last minute in November.