SINGAPORE - US President Donald Trump said he had forged a "good relationship" with North Korean leader Kim Jong Un at the start of a historic summit in Singapore on Tuesday, as the two men sought ways to end a nuclear standoff on the Korean peninsula.Should they succeed in making a diplomatic breakthrough, it could bring lasting change to the security landscape of Northeast Asia, like the visit of former US President Richard Nixon to China in 1972 led to the transformation of China."There will be challenges ahead," Kim said, but he vowed to work with Trump. Both men sat alongside each other against a backdrop of North Korean and US flags, with Kim beaming broadly as the US president gave him a thumbs up.The combatants of the 1950-53 Korean War are technically still at war, as the conflict, in which millions of people died, was concluded only with a truce.With cameras of the world's press trained on them, Trump and Kim displayed an initial atmosphere of bonhomie.Both men looked serious as they got out of their limousines for the summit at the Capella hotel on Singapore's Sentosa, a resort island with luxury hotels, a casino, man-made beaches and a Universal Studios theme park.But they were soon smiling and holding each other by the arm, before Trump guided Kim to the library where they held a meeting with only their interpreters. Trump had said on Saturday he would know within a minute of meeting Kim whether he would reach a deal.After some initial exchanges lasting around 40 minutes, Trump and Kim emerged, walking side-by-side through the colonnaded hotel before re-entering the meeting room, where they were joined by their most senior officials.Kim was heard telling Trump through a translator: "I think the entire world is watching this moment. Many people in the world will think of this as a scene from a fantasy... science fiction movie."Asked by a reporter how the meeting was going, Trump said: "Very good. Very, very good. Good relationship."Kim also sounded positive about the prospects."We overcame all kinds of skepticism and speculations about this summit and I believe that this is good for the peace," he said. "I believe this is a good prelude for peace."Trump was joined by Secretary of State Mike Pompeo, National Security Adviser John Bolton, and John Kelly, White House Chief of Staff, for the expanded talks, while Kim's team included former military intelligence chief Kim Yong Chol, foreign minister Ri Yong Ho and Ri Su Yong, vice chairman of the ruling Workers' Party.