North Korean state media has hailed the impromptu visit made by US President Donald Trump to the country as "an amazing event".
On Sunday, Mr Trump became the first sitting US president to set foot in North Korea, accompanied by leader Kim Jong-un.
Mr Trump had earlier tweeted asking Mr Kim if he would like to meet while the US president was in South Korea.
On Monday, KCNA carried extensive coverage of the unprecedented meeting.
The North Korean state news agency said the meeting "at the suggestion of Trump", was "historic".
It said that in the 66 years since the Armistice agreement - which ended fighting in the Korean War - "there happened such an amazing event of the top leaders of the DPRK and the US exchanging historic handshakes at Panmunjom, place that had been known as the symbol of division".
The Democratic People's Republic of Korea (DPRK) is North Korea's official name.
Confirming comments from Mr Trump, KCNA said the leaders had agreed to "keep in close touch in the future" and to "resume and push forward productive dialogues for making a new breakthrough in the denuclearization of the Korean peninsula and in the bilateral relations".
North Koreans rarely receive news of the outside world and the heavily controlled media has depicted the US as its most hated enemy for decades.
So images of the US president walking into the North as a friend of Mr Kim will be extraordinary for ordinary North Koreans to see.
What happened at the DMZ?
Mr Trump was on a scheduled visit to South Korea, following the G20 summit in Japan.
He was scheduled to hold talks about the stalled North Korea nuclear negotiations with South Korea's President Moon Jae-in and to visit the demilitarised zone (DMZ), the buffer area between the two Koreas since the end of the Korean War.
On Saturday, he tweeted a message to Mr Kim, suggesting he could "meet him at the Border/DMZ just to shake his hand and say Hello(?)!"
After a day of speculation and backroom diplomacy, Mr Trump and Mr Moon confirmed on Sunday that Mr Kim had accepted the invitation and they would have a "brief handshake".
They arrived at the border zone in the early afternoon and after a short tour, they and Mr Kim approached the military demarcation line.
"Good to see you again. I never expected to meet you at this place," a smiley Mr Kim told Mr Trump through an interpreter in an encounter broadcast live on international television.
"Big moment," Mr Trump said, "tremendous progress."
Mr Kim invited Mr Trump to step over into North Korea, saying he would be the first US president to do so. The US president then spent a few minutes on the north side before
Looking relaxed, Mr Kim crossed into South Korea and alongside Mr Trump said: "I believe this is an expression of his willingness to eliminate all the unfortunate past and open a new future."
For a brief moment, Mr Trump and Mr Kim were joined by South Korea's President Moon Jae-in, an unprecedented three-way gathering.
Who is sending aid to North Korea?
Speaking next to Mr Trump in a rare statement to the press, Mr Kim said the meeting was a symbol of their "excellent" relationship.
Calling their friendship "particularly great", Mr Trump - who once referred to Mr Kim as "little rocket man" - said it was a "great day for the world" and that he was "proud to step over the line" between the Koreas.
The encounter had initially been billed as a short greeting but Mr Trump and Mr Kim ended up talking for almost an hour in a building known as the Freedom House, on the South Korean side of Panmunjom, the "truce village" inside the DMZ.
What to make of the meeting?
Mr Trump and Mr Kim agreed that negotiators will meet in the next weeks to resume discussions about North Korea's nuclear programme, Mr Trump told reporters, saying he was "not looking for speed [but] looking to get it right".
Sanctions on North Korea, he added, would remain in place though he appeared to leave open the possibility of easing them as part of the talks. Mr Trump also said he had invited Mr Kim to visit Washington.
But analysts have questioned whether the meeting will result in any substantive progress.
How are US-North Korea relations?
Negotiations with North Korea to try to convince it to abandon its controversial nuclear programme reached a peak last year when Mr Trump and Mr Kim had a historic meeting in Singapore.
They both committed to the "complete denuclearisation" of the Korean peninsula, but without clarifying what that meant.
It was hoped their second meeting, in Hanoi in February, would make some concrete agreement about North Korea handing over its nuclear programme in exchange for some of the tight sanctions against it being lifted.
But those talks ended with no deal, as they failed to agree on the pace at which sanctions should be eased. Since then the negotiations have stalled, though Mr Kim and Mr Trump have exchanged letters recently.
