U.S. President Donald Trump said his historic summit with North Korean leader Kim Jong Un in Singapore on Tuesday would show if a "real deal" could happen, as both sides sought to narrow differences over how to end a nuclear standoff on the Korean peninsula.While Trump was optimistic about prospects for the first-ever meeting of sitting U.S. and North Korean leaders, U.S. Secretary of State Mike Pompeo injected a note of caution, saying it remained to be seen if Kim was sincere about his willingness to denuclearize.Officials of the two sides held last-minute talks to lay the groundwork for the summit of the old foes, an event almost unthinkable just months ago, when they were exchanging insults and threats that raised fears of war.Staff-level meetings between the United States and North Korea were going "well and quickly," Trump said in a message on Twitter on Tuesday.But he added: "In the end, that doesn't matter. We will all know soon whether or not a real deal, unlike those of the past, can happen!"After a flurry of diplomatic overtures that eased tension, the leaders are headed for a history-making handshake that U.S. officials hope could eventually lead to the dismantling of a North Korean nuclear program that threatens the United States.Trump will hold a one-on-one meeting with Kim on the resort island of Sentosa, before they are joined by officials and have lunch together, the White House has said."I just think it's going to work out very nicely," Trump said on Monday, although gaps remain over what denuclearisation would entail.Pompeo told reporters the event should set the framework for "the hard work that will follow," insisting that North Korea had to move toward complete, verifiable and irreversible denuclearize.North Korea, however, has shown little appetite for surrendering nuclear weapons it considers vital to the survival of Kim's dynastic rule.Sanctions on North Korea would remain in place until that happened, Pompeo said. "If diplomacy does not move in the right direction ... those measures will increase."He added: "North Korea has previously confirmed to us its willingness to denuclearize and we are eager to see if those words prove sincere."The White House said later that discussions with North Korea had moved "more quickly than expected" and Trump would leave Singapore on Tuesday night after the summit, rather than Wednesday, as scheduled earlier.Kim is due to leave on Tuesday afternoon, a source involved in the planning of his visit has said.One of the world's most reclusive leaders, Kim visited Singapore's waterfront on Monday, smiling and waving to onlookers, adding to a more affable image that has emerged since his April summit with South Korean leader Moon Jae-in.The Swiss-educated leader, who is believed to be 34, has not left his isolated country since taking office in 2011, apart from visiting China and the South Korean side of the border Demilitarized Zone, which separates the two Koreas.Just a few months ago, Kim was an international pariah accused of ordering the killing of his uncle, a half-brother and scores of officials suspected of disloyalty.'CHANGED ERA'The summit was part of a "changed era," North Korea's state-run KCNA news agency said in its first comments on the event.Talks would focus on "the issue of building a permanent and durable peace-keeping mechanism on the Korean peninsula, the issue of realizing the denuclearization of the Korean peninsula and other issues of mutual concern," it added.Ahead of the summit, North Korea rejected unilateral nuclear disarmament, and KCNA's reference to denuclearization of the peninsula has historically meant it wants the United States to remove a "nuclear umbrella" protecting South Korea and Japan.The 1950-53 Korean War was concluded only with a truce, not a peace treaty, leaving the combatants technically still at war.Many experts on North Korea remain skeptical Kim will ever completely abandon nuclear weapons, believing his engagement aims to get the United States to ease crippling sanctions."The process could be doomed before it begins," said Kelsey Davenport of the Arms Control Association, adding that a common understanding of denuclearization was key to success.