The talks were expected to continue through until the end of Tuesday, and are focused on what would be the substance of a potential summit between Trump and Kim – the issue of North Korea’s nuclear weapons programme.

“I truly believe North Korea has brilliant potential and will be a great economic and financial Nation one day,” Trump said on Twitter.

“Kim Jong-un agrees with me on this. It will happen!,” the president said, confirming that a US team “has arrived in North Korea to make arrangements for the summit” between himself and North Korean leader Kim.

His upbeat language contrasted sharply to that of only three days earlier, when Trump cancelled the planned summit, citing “open hostility” from the North.

An extraordinary flurry of diplomacy since then – much of it led by South Korea – appears to have put the meeting back on track.

Kim and South Korean President Moon Jae-in met Saturday at the Panmunjom border truce village, in a surprise bid to salvage the June 12 summit planned for Singapore.

Announcing the lower-level talks held Sunday, US State Department spokeswoman Heather Nauert said: “We continue to prepare for a meeting between the president and North Korean leader Kim Jong-un.”

The Washington Post reported that the US delegation met with North Korean Vice Foreign Minister Choe Son-hui.

The United States currently has no ambassador to South Korea, even as it takes up one of the most delicate diplomatic challenges in years.

Sung Kim was joined by Allison Hooker, the Korea specialist on the National Security Council, and an official from the US Defence Department.

Randall Schriver, the assistant secretary of defence for East Asia and one of the officials who accompanied US Secretary of State Mike Pompeo to Pyongyang earlier this month, also is in Seoul. However, it could not be immediately confirmed whether he was the Pentagon official involved in Sunday’s talks.

Sung Kim, who was born in South Korea and was a key diplomat in the 2005 six-party talks, served as ambassador to South Korea from 2011 to 2014, then became special representative for North Korea policy.

His North Korean counterpart, Choe, also has years of experience working on these issues and is well connected within the North Korean hierarchy.

She has also served as a nuclear negotiator and led the division for US affairs in the North Korean Foreign Ministry until being promoted to vice foreign minister this year.

The daughter of a former premier, she is also thought to have direct access to Kim.

Given all the ups and downs with the summit, many analysts were relieved to hear that the administration had enlisted Sung Kim to help, especially given the retirement of fellow seasoned diplomat Joseph Yun earlier this year.

“This is a great step,” said Vipin Narang, a nuclear non-proliferation expert at the Massachusetts Institute of Technology, noting that the summit preparation was best handled by experts behind the scenes rather than in public forums such as Twitter.

In addition to the border talks, White House spokeswoman Sarah Huckabee Sanders said a “pre-advance team” left for Singapore on Sunday morning to work on logistics for a possible summit.

Kim Chang-son, a senior official of North Korea’s State Affairs Commission, was believed to have arrived in Beijing on Monday, before continuing onto Singapore, Kyodo reported.

US officials said the United States and North Korea would focus on a proposed shipment overseas of nuclear warheads possessed by Pyongyang when the two sides hold preparatory talks.

But it was not known if they can reach an agreement on the issue, given the North’s reluctance to meet the US demand that it ship an estimated up to 20 warheads overseas soon as part of measures to achieve a complete, verifiable and irreversible denuclearisation of North Korea.

According to the US officials, speaking on condition of anonymity, North Korea has expressed reluctance to ship all of its nuclear weapons and missiles outside the country.

If US and North Korean officials are unable to reach a deal in preparatory talks, a decision could be left to a Trump-Kim summit, according to the US officials.

The officials were also expected to discuss how Pyongyang would scrap weapons-grade plutonium, highly enriched uranium and other nuclear-related material, they said.

Earlier on Sunday, Moon said he and North Korea’s Kim had agreed during a surprise meeting on Saturday that the North Korea-US summit must be held.

In their Saturday meeting, Kim reaffirmed his commitment to “complete” denuclearisation of the Korean Peninsula and to a planned meeting with Trump, 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 programme.

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 November 29.

Trump initially scrapped the June 12 summit after repeated threats by North Korea to pull out over what it saw as confrontational remarks by US officials demanding unilateral disarmament.

North Korea had sharply criticised suggestions by Trump’s 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 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 reported, citing an unidentified foreign affairs source.

Agence France-Presse, Reuters, The Washington Post, Kyodo, USA Today