It is the third time the two leaders have met, and the first since a failed summit on the North’s nuclear program in Vietnam earlier this year.
Trump initiated the meeting in a tweet on Saturday.
Kim said he was “surprised” by Trump’s request to meet, and called the US President’s short walk into North Korea “a very courageous and determined act”.
“Stepping across that line was a great honour,” Trump said.
“It’s just an honour to be with you,” Trump said later in a meeting with Kim, adding that his willingness to meet on short notice “made us both look good”.
“The relationship that we’ve developed has meant so much to so many people,” Trump said.
Kim said the meeting with Trump would “positively” affect their future moves and said their relationship was “great”.
The historic meeting came as Trump seeks to make a legacy-defining nuclear deal with the North.
Kim said the brief visit to North Korean territory improved ties, while Trump said it “feels great” to be the first US President to step into North Korea, and hailed “great friendship” with Kim.
Before meeting Kim, Trump met several dozen troops stationed at the Korean DMZ separating South and North Korea and telling them, “We’re with you all the way.”
Peering into North Korea from Observation Post Ouellette before the meeting Kim, Trump was briefed on the North’s extensive artillery across the border that threatens the 35 million residents of Seoul, just over two dozen miles away.
“All accessible by what they have in the mountains,” Trump said.
Trump invited Kim on Saturday to meet him at the border for a symbolic handshake. He expressed openness to briefly crossing into North Korean territory if Kim accepted.
Trump claimed to reporters that, after his first meeting with Kim, “all of the danger went away”. He was accompanied on the visit by South Korean President Moon Jae-in.
He departed Seoul aboard the Marine One presidential helicopter shortly after Moon announced on Sunday, alongside Trump, that Kim had accepted Trump’s invitation to meet at the heavily fortified site at the Korean border village of Panmunjom.
Trump told reporters before departing that he looked forward to seeing Kim and to “shake hands quickly and say hello”.
The meeting between Trump and Kim would mark yet another historic first in the yearlong rapprochement between the US and North Korea, which technically are still at war.
It also would mark the return of face-to-face contact between the leaders since negotiations to end the North’s nuclear program broke down during a summit in Vietnam in February.
Moon praised the two leaders for “being so brave” to hold the meeting and said, “I hope President Trump will go down in history as the President who achieves peace on Korean Peninsula.”
Trump sought to tamp down expectations by saying the meeting would be “very short”.
He told reporters at a news conference with Moon that he and Kim would “just shake hands quickly and say hello” at the historic meeting at the Korean border village.
“Virtually a handshake, but that’s OK. A handshake means a lot,” he said.
Every president since Ronald Reagan has visited the 1953 armistice line, except for George H.W. Bush, who visited as vice-president.
Officials spent Sunday morning working out logistical and security details, Trump said during an earlier appearance with Moon.
The invitation, while long rumoured in diplomatic circles, still came across as an impulsive display of showmanship by a President bent on obtaining a legacy-defining nuclear deal. North Korea had responded by calling the offer a “very interesting suggestion”.
Presidential visits to the DMZ are traditionally carefully guarded secrets for security reasons. Trump claimed before flying from Japan to South Korea that he wasn’t even sure Kim was in North Korea to accept the invitation.
“All I did is put out a feeler, if you’d like to meet,” Trump said in Japan. He added, somewhat implausibly: “I just thought of it this morning.”
Before arriving in Seoul, Trump said at a news conference in Japan that he’d “feel very comfortable” crossing the border into North Korea if Kim showed up, saying he’d “have no problem” becoming the first US president to step into North Korea.
What is the DMZ?
* The DMZ marks where the 1950-53 Korean War – when China and North Korea battled UN forces led by the United States – ended with an armistice, not a treaty.
* It is a two-kilometre-wide, 250-kilometre-long buffer, stretching coast to coast across the peninsula, lined by both sides with razor wire, heavy armaments and tank traps.
* It is 60 kilometres from the South Korean capital Seoul and 210 kilometres from the North Korean capital Pyongyang.
* Inside the DMZ is a Joint Security Area (JSA). The so-called peace village of Panmunjom, where the armistice that halted the Korean War was signed in 1953, is located in the 800-metre-wide and 400-metre-long JSA zone.
* A Military Demarcation Line (MDL) marks the boundary between the two Koreas.
* Panmunjom is a cluster of distinctive bright blue buildings. The two Koreas have their own liaison offices and conference halls, on each side of the MDL in Panmunjom.
* Under a 1953 deal, the UN Command and the North Korean military were allowed to dispatch no more than 35 troops to the JSA, and each of them can only possess one pistol or non-automatic rifle. But the number of soldiers and weapons increased as relations worsened.
* The troops face each across the MDL in Panmunjom.
* The first inter-Korean summit in more than a decade was held in Panmunjom last year.
* After a third summit between the two Koreas in September, the two sides withdrew firearms from the JSA and cut the number of troops back to the original 35.
* Vast stretches of the DMZ have been no man’s land for more than 60 years, where wildlife has flourished undisturbed. Other parts of it offer an unsettling mix of military installations and tourist attractions.
* According to the UN command, more than 105,000 tourists visited the JSA from the South in 2017, while nearly 30,000 visited from the North.
* South Korea estimates the North operates about 160 guard posts along the DMZ and the South has 60. After a military deal last year, 11 of them from each side were demolished.
* The DMZ is littered with landmines planted over the decades – as many as 970,000 in the southern part alone, according to Landmine and Cluster Munition Monitor, a Geneva-based civic group.
* For years, both sides blared propaganda broadcasts over the DMZ into each other’s territory. The broadcasts ended after last year’s military agreement.
Bloomberg, AP, Reuters