The North Korean leader made the comments during a third historic summit with South Korean president Moon Jae-in upon in Pyongyang.
Thousands of North Koreans holding flower bouquets waved national and unification flags and an honour guard quick-marched into tight lines as the two leaders met on Tuesday.
Here’s what you need to know as talks between Kim and Moon get underway.
What’s it all about?
Essentially, the two leaders have stated a desire to make progress in nuclear diplomacy.
Amid the pomp and smiles, Moon will be looking to settle some lofty goals, including resolving a deadlocked nuclear challenge, easing a military standoff and promoting peace on a peninsula many feared was close to war last year.
The South Korean leader said ahead of his trip that he will push for “irreversible, permanent peace” and for better dialogue between Pyongyang and Washington during “heart-to-heart” talks with his North Korean counterpart.
Why is this summit different?
Since taking office in May last year, Moon has met Kim twice – at the Koreas’ shared border village of Panmunjom.
Moon’s first Pyongyang trip makes him the third South Korean leader to visit North Korea’s capital for an inter-Korean summit since the peninsula was divided into a Soviet-backed North and US-backed South at the end of the Second World War.
The two countries fought a bloody three-year war five years later after a North Korean sneak attack.
The leaders are both pushing a reluctant Washington to sign off on formally ending the war with a peace treaty.
Moon’s two late liberal predecessors, Kim Dae-jung and Roh Moo-hyun, went to Pyongyang in 2000 and 2007, respectively, to meet Kim’s dictator father Kim Jong Il.
Those trips produced a slew of inter-Korean rapprochement projects. But they were later suspended after conservatives took power in Seoul with hard-line policies toward the North.
Kim Jong Un took office in late 2011 upon the death of his father.
What will happen?
Moon is to meet Kim at least twice — later on Tuesday and then again on Wednesday before returning home on Thursday.
“This summit would be very meaningful if it yielded a resumption of North Korea-US talks,” Moon said before his departure.
“It’s very important for South and North Korea to meet frequently, and we are turning to a phase where we can meet anytime we want.”
While presiding over a meeting with top advisers on Monday, Moon said he “aims to have lots of heart-to-heart talks” with Kim and achieve “irreversible, permanent peace that is not shaken by international politics”.
To achieve such a peace, Moon said he will focus during the summit on easing military tensions between the Koreas and promoting a North Korea-U.S. dialogue on denuclearisation issues.
Moon said he wants “to find a middle ground between a US request for (North Korea’s) denuclearisation and the North’s request for corresponding measures such as ending hostile relations and security assurances.”
The South Korean leader’s chief of staff, however, played down the chance that the summit with Kim will produce major progress.