SEOUL/WASHINGTON (Reuters) - U.S. President Donald Trump said on Sunday a U.S. team had arrived in North Korea to prepare for a proposed summit between him and North Korean leader Kim Jong Un, which Trump pulled out of last week before reconsidering.

Earlier, the U.S. State Department said U.S. and North Korean officials had met at Panmunjom, a village in the Demilitarized Zone (DMZ) that runs along the heavily armed border between North and South Korea.

"Our United States team has arrived in North Korea to make arrangements for the Summit between Kim Jong Un and myself," Trump wrote on Twitter, in Washington's first confirmation that U.S. officials had entered North Korea for the talks.

"I truly believe North Korea has brilliant potential and will be a great economic and financial Nation one day. Kim Jong Un agrees with me on this. It will happen!" Trump added.

In addition to those talks, White House spokeswoman Sarah Sanders said a "pre-advance team" left for Singapore - where the summit has been expected to take place - on Sunday morning to work on logistics.

Earlier on Sunday, South Korean President Moon Jae-in said he and North Korea's Kim had agreed during a surprise meeting on Saturday that the North Korea-U.S. summit must be held.

The weekend talks were the latest twist in a week of diplomatic ups and downs over the prospects for an unprecedented U.S.-North Korea summit, and the strongest sign yet that the two Koreas' leaders are trying to keep the meeting on track.

North Korea has faced years of economic sanctions over its nuclear and missile programs since it conducted its first nuclear test in 2006.

The United States has struggled to slow the isolated country's weapons programs, which have become a security priority for Washington given Pyongyang's promise to develop a nuclear-tipped missile capable of hitting the U.S. mainland.

A U.S. official told Reuters that Sung Kim, the former U.S. ambassador to South Korea, would lead an American delegation to meet North Korean officials at the border. Pentagon official Randall Schriver was part of the U.S. team, the official said.

The Washington Post first reported that the team, which also included Allison Hooker, the Korea expert on the White House National Security Council, met with Choe Son Hui, the North Korean vice foreign minister.

The Post said the talks at the border would continue on Monday and Tuesday at Tongilgak, the North's building in Panmunjom, where the truce suspending the 1950-53 Korean War was signed.

In their meeting on Saturday, Kim reaffirmed his commitment to "complete" denuclearisation of the Korean Peninsula and to a planned summit with Trump, Moon told reporters in Seoul.

"Chairman Kim and I have agreed that the June 12 summit should be held successfully, and that our quest for the Korean Peninsula's denuclearisation and a perpetual peace regime should not be halted," Moon said.

Moon acknowledged Pyongyang and Washington may have differing expectations of what denuclearisation 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 denuclearisation 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.

North Korea has tested dozens of missiles of various types in the past two years, including one launch of its largest-ever intercontinental ballistic missile, which is theoretically capable of hitting anywhere in the United States, on Nov. 29.

Nuclear North Korea: https://tmsnrt.rs/2Kql12i

Nuclear testing site: https://tmsnrt.rs/2wGynpf

MISTRUST ON BOTH SIDES

American officials are sceptical that Kim will ever fully abandon his nuclear arsenal. Moon said North Korea was not convinced it could 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 denuclearises," Moon said.

Moon met Trump in Washington on Tuesday 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.

Trump on Thursday scrapped the summit after repeated threats by North Korea to pull out over what it saw as confrontational remarks by U.S. officials demanding unilateral disarmament.

On May 16, North Korea criticized U.S. national security adviser John Bolton, who had called for North Korea to quickly give up its nuclear arsenal in a deal that would mirror Libya's abandonment of its programme for weapons of mass destruction.

Libyan leader Muammar Gaddafi was deposed and killed by NATO-backed militants in 2011 after halting his nascent nuclear programme.

Trump dismissed the so-called Libya model. Sanders, his spokeswoman, told Fox News on May 15: "This is the President Trump model. He’s going to run this the way he sees fit."

Kim had requested a meeting with Moon to clarify what the "Trump model" meant, Yonhap news agency of South Korea reported, citing an unidentified foreign affairs source.

Kim and Trump's initial decision to meet followed months of war threats and insults between the leaders over the North's nuclear programme.

Trump said on Saturday he was still looking at a June 12 summit in Singapore and that talks were going well.

(Reporting by Hyonhee Shin in Seoul and Lesley Wroughton in Washington; Additional reporting by Matt Spetalnick, Katanga Johnson, Doina Chiacu in Washington, Josh Smith, Soyoung Kim, Choonsik Yoo and Jeongmin Kim in Seoul and Ben Blanchard and Elias Glenn in Beijing; Writing by Doina Chiacu and Arshad Mohammed; Editing by Frances Kerry and Peter Cooney)