On Friday, Kim and South Korean President Moon Jae-in vowed "complete denuclearisation" of the Korean peninsula in the first inter-Korean summit in more than a decade, but the declaration did not include concrete steps to reach that goal.
North Korea's state media had said before the summit that Pyongyang would immediately suspend nuclear and missile tests, scrap its nuclear test site and instead pursue economic growth and peace.
Kim told Moon that he would soon invite experts and journalists from the United States and South Korea to "transparently open to the international community" the dismantling of the facilities, the Blue House said.
"Kim said if the United States holds dialogue with the North, they would realise that he's not the kind of person who would fire a nuclear missile toward the South, over the Pacific or targeting the United States," Moon's press secretary Yoon Young-chan told a news briefing.
"If the United States meets often and builds trust with us and promises an end of war and non-aggression, why would we lead a difficult life?" Yoon reported Kim as saying.
Kim said there were two additional, larger tunnels that remain "alive and well" at the Punggye-ri test site beyond the existing one, which experts have said had collapsed after repeated explosions, rendering much of the site useless.
Kim's promise shows his willingness to "preemptively and actively" respond to inspection efforts to be made as part of the denuclearisation process, Yoon said.
To facilitate future cross-border cooperation, Kim pledged to scrap the unique time zone Pyongyang created in 2015. He said the North would move its clocks forward 30 minutes to be in sync with the South, nine hours ahead of Greenwich Mean Time.
Kim also reaffirmed that he would not use military force against the South and raised the need for an institutional mechanism to prevent unintended escalations, Yoon said.
Late Saturday, U.S. President Donald Trump told Moon in a phone call that he was pleased the leaders of the two Koreas reaffirmed the goal of complete denuclearisation during their summit, Seoul officials said on Sunday.
Moon and Trump agreed on the need for an early summit between Trump and Kim, and explored two to three potential locations, the Blue House said.
A senior U.S. official has said Singapore is being considered as a possible venue for the Trump-Kim summit.
"Trump said it was good news for not only the two Koreas but the whole world that they affirmed the goal of realising a nuclear-free Korean peninsula through a complete denuclearisation," South Korea's presidential Blue House said. "Trump was looking forward to talks with Kim and there would be a very good result."
Trump, who called the 75-minute chat "a long and very good talk" on Twitter, said his summit with Kim would take place sometime in the next three to four weeks.
"It's going be a very important meeting, the denuclearisation of the Korean peninsula," he said at a campaign rally in Washington, Michigan, on Saturday.
The White House said Trump and Moon during the call "emphasized that a peaceful and prosperous future for North Korea is contingent upon its complete, verifiable, and irreversible denuclearisation."
Trump had also informed Japanese Prime Minister Shinzo Abe that he would urge North Korea to promptly resolve its abductions of Japanese citizens, the White House said.
Most of the specific commitments outlined in the official declaration signed by Kim and Moon focused on inter-Korean relations and did not clear up the question of whether Pyongyang is willing to give up its arsenal of nuclear weapons and ballistic missiles.
It made rare mentions of the denuclearisation discussion, but did not go into detail, instead highlighting the broad themes of peace, prosperity, and Korean unity.
"At the talks both sides had a candid and open-hearted exchange of views on the matters of mutual concern including the issues of improving the North-South relations, ensuring peace on the Korean Peninsula and the denuclearisation of the peninsula," KCNA said.
It added that the night wrapped up with a dinner that had an "amicable atmosphere overflowing with feelings of blood relatives."
The declaration earned guarded but optimistic praise from world leaders, including Trump, who said on Friday that only time would tell, but that he did not think Kim was "playing."
"It's never gone this far. This enthusiasm for them wanting to make a deal ... We are going to hopefully make a deal."
Still, Trump said he would maintain pressure on North Korea and "not repeat the mistakes of past administrations."
In Sydney on Saturday, Australian Prime Minister Malcolm Turnbull praised Trump's negotiations on North Korea and said he helped bring the two Korean leaders together.
"I have given him that credit because Donald Trump has taken a very, very strong, hard line on the denuclearisation issue and he has been able to bring in the support of the global community and, in particular, China," Turnbull told a televised news conference, referring to "overwhelming" economic ties between China and North Korea.
"What we've now got to do is not relent on the economic pressure until that goal is achieved," he said.
Australia will send a military aircraft to monitor North Korean vessels suspected of transferring illicit goods in defiance of U.N. sanctions, he said.
Iran, facing a possible U.S. exit from its nuclear deal with world powers, welcomed the inter-Korean summit, but said Washington was not a "qualified" partner in the negotiations.
"Iran sees (the summit) as an important step in the right direction that can contribute to lasting regional and global peace and security," Iranian foreign ministry spokesman Bahram Qasemi was quoted as saying by state media.
"The U.S. government is not a credible actor, doesn't comply with its international obligations and doesn't qualify to take part in arrangements between countries," Qasemi added.
An editorial in the official China Daily on Saturday said denuclearisation could end hostilities between the two sides and "usher in a new era of development" on the peninsula, but noted Friday's declaration lacked a plan for achieving the goal.
"The denuclearisation of the peninsula, written into the Panmunjom Declaration, is only a prospect with no specific plan. That is because such specifics can be reached only between the US and North Korea, and South Korea has only limited authority to bargain," it said.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)