The Korean Central News Agency reports that the two leaders expressed great satisfaction over the results of their talks.
The pair made history previous year when they met in Singapore, a country in Asia, as it was the first time a serving United States president had met with the North Korean leader.
Trump stepped across Panmunjom's military demarcation line into North Korea with Kim, becoming the first sitting American president to set foot in the Hermit Kingdom.
"The top leaders of the DPRK and the U.S. exchanging historic handshakes at Panmunjom" was an "amazing event", KCNA said, describing the truce village as a "place that had been known as the symbol of division".
Some 28,500 USA servicemembers are stationed in South Korea, which remains technically at war with the North.
South Korea has also said re-opening the Kaesong industrial park and tours to Mount Kumgang, two inter-Korean projects closed as tensions ramped up, could expedite the North's denuclearisation. Trump became the first sitting U.S. president to step into the North and invited Kim to visit the White House.
President Trump declared that a nuclear North Korea was not acceptable and posed a threat to the United States.
"The president, by getting together with Chairman Kim today, broke through and was able to get us the opportunity to get back to the negotiating table, which I'm excited about", Pompeo said.
The meeting dominated the pages of the official Rodong Sinmun newspaper on Monday.
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The DMZ is the world's most heavily fortified border.
Shin Beom-chul, an analyst at the Asan Institute of Policy Studies, said the KCNA report was "typical North Korean propaganda that glorified Kim as leading the tremendous changes in geopolitics". "That's news to me". The official also confirmed that Youn Kun-young, the director of the presidential state affairs planning and monitoring office headed the preparations for the DMZ meet-up, including logistics, protocol and media coverage.
The first Trump-Kim summit took place in a blaze of publicity in Singapore previous year but produced only a vaguely worded pledge about denuclearisation.
Then they met in Hanoi, Vietnam in February, but talks broke down without any joint agreement as Kim pushed for sanctions relief and the U.S. pushed for denuclearisation.
The development comes just a day after US President Donald Trump and North Korean leader Kim Jong met at the DMZ and agreed to resume working-level talks on the Pyongyang's nuclear program.
The Times, which noted that U.S. officials previously said they would never support such a plan, said officials in the administration hope the idea "might create a foundation for a new round of negotiations" with North Korea and noted that the administration's current goal is still to fully denuclearize the country.
Vipin Narang of the Massachusetts Institute of Technology said the North was portraying Kim as "being courted by Trump".
"I'd invite him right now-to the White House, absolutely", Trump said.
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