North Korea on Monday described the weekend meeting between its leader Kim Jong Un and US President Donald Trump in the Demilitarized Zone as "historic" and "amazing". The two leaders agreed to "resume and push forward productive dialogues for making a new breakthrough in the denuclearisation of the Korean peninsula", the official Korean Central News Agency said. After a Twitter invitation by the US president on Saturday, the two men met a day later in the strip of land that has divided the peninsula for 66 years since the end of the Korean War, when their countries and their allies fought each other to a standstill. Kim and Trump shook hands over the concrete blocks dividing North and South before Trump walked a few paces into Pyongyang's territory -- the first US president ever to set foot on North Korean soil. "The top leaders of the DPRK and the US 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". The meeting took place "at the suggestion of Trump", it added. The impromptu meeting in the DMZ -- after Trump issued an invitation on Twitter the day before -- came with negotiations between Pyongyang and Washington over the North's nuclear programme at a deadlock. Their first summit took place in a blaze of publicity in Singapore last year but produced only a vaguely worded pledge about denuclearisation. A second meeting in Vietnam in February that intended to put flesh on those bones collapsed after the pair failed to reach an agreement over sanctions relief and what the North was willing to give in return. Trump said after the meeting that they had agreed working-level talks on the North's arsenal would take place within weeks. KCNA said Kim and Trump discussed "issues of mutual concern and interest which become a stumbling block in solving those issues". The two leaders "agreed to keep in close touch in the future", it added. KCNA cited Kim lauding their "good personal relations," saying they would "produce good results unpredictable by others and work as a mysterious force overcoming manifold difficulties and obstacles in the future, too".