U.S. officials crossed into North Korea on Sunday to hold talks on preparations for a possible summit, a U.S. newspaper reported, as North Korean leader Kim Jong Un reaffirmed his commitment to meet with U.S. President Donald Trump. Both Pyongyang and Washington are pressing ahead on plans for a summit after Trump pulled out of the proposed June 12 meeting on Thursday, only to reconsider the decision the next day. South Korean President Moon Jae-in said earlier that he and North Korea's Kim had agreed during a surprise meeting on Saturday that the possible North Korea-U.S. summit must be held. The weekend meetings were the latest dramatic turn in a week of diplomatic ups and downs over the prospects for an unprecedented summit between the United States and North Korea, and the strongest sign yet that the leaders of the two Koreas are trying to keep the meeting on track. The Washington Post, citing a person familiar with the arrangements, said Sung Kim, a former U.S. ambassador to South Korea and former nuclear negotiator with the North, was leading the preparations on the U.S. side. The American diplomat crossed into North Korean territory with Allison Hooker, the Korea expert on the White House National Security Council, as well as a Defense Department official, the Post said. They met with Choe Son Hui, the North Korean vice foreign minister, the Post said. A U.S. official confirmed to Reuters there were plans for Sung Kim, who currently is U.S. ambassador to the Philippines, to lead an American delegation to meet North Korean officials on the border this weekend for summit preparations in the event that the Singapore meeting goes ahead. Pentagon official Randall Schriver was part of the U.S. team for talks at the border on the summit agenda, the official said. However, the official did not know whether the U.S. representatives were in place. The Post said the meetings were expected to continue on Monday and Tuesday. The White House did not immediately comment on the planning talks in the region. In their Saturday meeting, Kim reaffirmed his commitment to "complete" denuclearization of the Korean Peninsula and to a planned meeting with Trump, Moon said. "Chairman Kim and I have agreed that the June 12 summit should be held successfully, and that our quest for the Korean Peninsula's denuclearization and a perpetual peace regime should not be halted," Moon said. Moon acknowledged Pyongyang and Washington may have differing expectations of what denuclearization means and he urged both sides to hold working-level talks to resolve their differences. The United States has demanded the "complete, verifiable, and irreversible" dismantlement of North Korea's nuclear weapons program. Pyongyang has rejected unilateral disarmament and has always couched its language in terms of denuclearization of the Korean Peninsula. In previous, failed talks, North Korea said it could consider giving up its arsenal if Washington removed its troops from South Korea and withdrew its so-called nuclear umbrella of deterrence from South Korea and Japan. MISTRUST ON BOTH SIDES American officials are skeptical that Kim will ever fully abandon his nuclear arsenal, and Moon said North Korea is not convinced it can trust security guarantees from the United States. "However, during the U.S.-South Korea summit, President Trump clearly emphasized that we may see not only the end of hostile relations but also economic cooperation if North Korea denuclearizes," Moon said. Moon returned to Seoul on Thursday morning after meeting Trump in Washington in an effort to keep the U.S.-North Korea summit on track. A senior South Korean official said later the two Koreas were discussing a possible non-aggression pledge and the start of peace treaty talks as a way of addressing Pyongyang's security concerns before U.S.-North Korean negotiations. A statement from North Korea's state news agency KCNA said Kim expressed "his fixed will" on the possibility of meeting Trump as previously planned. Kim and Trump's initial decision to meet followed months of war threats and insults between the leaders over the North's nuclear program. 'DOING VERY WELL' Trump said on Saturday he was still looking at a June 12 date for a summit in Singapore and that talks were progressing well. "We're doing very well in terms of the summit with North Korea," Trump said at the White House. "It's moving along very nicely. So we're looking at June 12th in Singapore. That hasn't changed. So, we'll see what happens." A White House team will leave as scheduled for Singapore this weekend to prepare for the possible summit, a White House spokeswoman said on Saturday. Trump cited North Korea's "open hostility" in a letter to Kim on Thursday cancelling the planned Singapore summit. That decision followed repeated threats by North Korea to pull out over what it saw as confrontational remarks by U.S. officials demanding unilateral disarmament. North Korea had sharply criticized suggestions by Trump\u2019s national security adviser, John Bolton, and Vice President Mike Pence that it could share the fate of Libya if it did not swiftly surrender its nuclear arsenal. Libyan leader Muammar Gaddafi was deposed and killed by NATO-backed militants in 2011 after halting his nascent nuclear program. North Korea\u2019s vice foreign minister called remarks by Pence about North Korea stupid and suggested the two countries could either meet for a summit or for a nuclear showdown.