In his speech, broadcast early Tuesday on state-run television, Kim urged the United States to take "corresponding measures" in exchange for denuclearization steps the North Korean dictator has claimed his country has taken since a year ago.
Talks between the USA and North Korea have made little progress since Trump and Kim held an unprecedented summit in June and signed to "work toward complete denuclearization of the Korean Peninsula", without defining the term or setting a deadline.
Since the Singapore summit where Kim committed to working toward denuclearization, talks between the U.S. and North Korea have stalled due to their differences over the sequencing of denuclearization.
Kim said that North Korea had already pledged not to make, use or spread nuclear weapons and had taken concrete steps to implement this.
The annual New Year's address is a tradition Mr Kim picked up from his grandfather, founder of the communist country, Kim Il-sung.
He called last year "a year of stirring events that witnessed a dramatic change unprecedented in the history of national division spanning more than seven decades".
The North Korean leader, who had been described by Trump as a "Little Rocket Man" with nuclear ambitions, humanized himself by taking a late night stroll on Singapore's modern streets the night before the summit that set off a social media firestorm.
Mr Kim also met with President Moon three times last year - twice at the border truce village of Panmunjom and once in the North's capital Pyongyang - and at the weekend vowed to meet Moon "frequently" this year.
His televised address came at the end of a year which saw a historic summit with Donald Trump in Singapore in June.
TV screens show US President Donald Trump, right, meeting with North Korean leader Kim Jong Un in Singapore.
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.
David Maxwell, a North Korea expert and senior fellow at the Foundation for Defense of Democracies think tank, called the speech and setting "a brilliantly crafted performance". North Korea seemingly seeks to include China, one of its closest allies, in the talks for more leverage, experts have noted.
"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.
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.
North Korea is entering the fourth year of a five-year economic plan that Kim announced with great fanfare at a rare congress of his ruling party in 2016.
"North Korea is prepared to strike a move, so it is requesting South Korea to actively convince the United Nations and the U.S. to alleviate or lift sanctions layered upon the state".
A next step could be the revamping of the Kaesong manufacturing park, that served as a main symbol of cooperation between two Koreas until it was shut down in response to a nuclear test and missile launch in February 2016. The program was considered an important source of foreign currency for the North.