In his New Year's address, Kim said there would be faster progress on denuclearization if the United States takes corresponding action.
"I am always ready to sit down again with the United States president at any time and will make efforts to produce an outcome that the global community would welcome", Kim said.
However, if the USA did not "keep its promise made in front of the whole world" and instead "insists on sanctions and pressures" on North Korea, "we may be left with no choice but to consider a new way to safeguard our sovereignty and interests".
It was in last year's New Year's message that Mr Kim announced North Korea would take part in the Winter Olympics hosted by the South, which led to a thaw in relations.
"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.
"If the United States takes honest measures and corresponding action to our leading and pre-emptive efforts, then relations will advance at a fast and excellent pace through the process of implementing definite and groundbreaking measures", he said.
Kim has warned Washington not to test North Koreans' patience with sanctions and pressure.
Kim's speech also points toward a hard year for the U.S.
In the address, Kim Jong-un highlighted last year's developments in inter-Korean and US-North Korea relations, while calling on his country to seek economic development and modernize its defense industry.
That resulted in a dramatic detente a year ago, including three summits with South Korean President Moon Jae-in, and the historic meeting with Trump in June.
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.
The North Korean leader is also indirectly demanding his neighbors to the South push the U.S. and U.N Security Council harder to lift sanctions in exchange for the two countries to resume inter-Korean cooperative projects, Cheong said.
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.
After a flurry of diplomatic activity, in April Kim Jong-un met South Korean President Moon Jae-in for a summit at the inter-Korean border.
Meanwhile, Trump used his New Year's message to brag about the "accomplishments" of his adminstatrion so far.
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.
At a summit with US President Donald Trump in Singapore in June the two signed a vaguely worded pledge on denuclearization of the Korean peninsula.
It came after a year of high tensions when the North made rapid progress in its weapons programmes and fears of conflict rose.
North Korea's media have slammed the USA for clinging to sanctions without honoring its promises to Pyongyang. Washington and Pyongyang appear to have interpreted what exactly this means differently.
However, there was a clear warning that the country is not ready to disarm unilaterally.
Although he said he wished to pursue economic development instead of nuclear missiles, Kim threatened to change course if the United States does not begin granting sanctions relief and making other reciprocal gestures in 2019.
It is thought the North Koreans will push for a quick second summit, as they like their chances of winning concessions from Mr Trump that they might not get from lower-level officials.