Pyongyang and Seoul also pledged to formally end the state of war between the two, which has been ongoing since a 1953 ceasefire agreement that brought to a halt large-scale hostilities.The office of the South Korean president said the outcome of Saturday’s surprise meeting will be announced on Sunday.Reporting from South Korea’s capital, Seoul, Al Jazeera’s Andrew Thomas said it was “symbolically important” that the talks were held on the north side of Panmunjom. Kim and South Korean President Moon Jae-in met in April in what was only the third meeting between the leaders of the two states. He has since said he is open to reinstating the talks. Less than a month after their historic summit, the leaders of North and South Korea have met again at a border village amid hopes that the on-again-off-again talks between Pyongyang and Washington will actually happen.US President Donald Trump on Thursday announced the cancellation of his planned meeting with North Korea’s Kim Jong-un, originally scheduled for June 12 in Singapore, citing “tremendous anger and open hostility” from North Korea. “This is the first time that a South Korean leader has crossed over into the North for substantial talks in 11 years,” he said. “After Trump cancelled the summit in Singapore, there was a lot of damage here in South Korea to [Moon’s] political capital, because it was seen that he was actually not holding so much influence over what was happening.“He’s certainly done his job to correct this perception.”The meeting on Saturday is the latest chapter in a long-running diplomatic effort to end North Korea’s nuclear weapons programme.Concerns grew earlier this month after North Korea responded to the US calling for the denuclearisation of the peninsula and a complete dismantling of the nuclear programme by threatening to pull out of the summit unless Washington offered something in return.Following Trump’s cancellation of the summit, North Korea issued a statement declaring it was still open to talks.“It was a very nice statement they put out,” Trump said at the White House.“We’re talking to them now. They very much want to do it. We’d like to do it,” he added. “We’ll see what happens – it (the summit) could even be the 12th [of June].”Meanwhile, a spokeswoman for Trump said on Saturday that a White House team is still heading to Singapore this weekend to work on logistics for the Trump-Kim summit, in case the meeting is reset.Sarah Huckabee Sanders said the “pre-advance team for Singapore will leave as scheduled in order to prepare should the summit take place”. (Courtesy Al Jazeera) “In the context of the on-again-off-again-maybe-on-again US-North Korea summit, it looks as though Moon has wasted no time. He’s hit the ground running and he’s doing everything he can to get that summit back on track.”Se-Woong Koo, publisher of the online magazine, Korea Expose, said he was “astonished” the surprise meeting took place.“It shows very clearly that the two Koreas are committed to engaging with each other and also with the US in hopes of bringing about peace here on the peninsula,” he told Al Jazeera. On Saturday, they spoke for two hours on the North Korean side of Panmunjom in the demilitarised zone and discussed how to implement their declaration following their April 27 meeting, as well as the proposed talks between Kim and Trump.“There is no reason why we should fight each other – we are one nation,” Kim said in a joint statement with Moon after that meeting.