Remain engaged in North Korea but firm on sanctions ahead of denuclearisation: Pompeo

US President Trump became the first sitting US president to set foot in North Korea on Sunday when he met its leader, Kim Jong Un, in the Demilitarized Zone (DMZ) between the two Koreas and agreed to resume stalled nuclear talks.

But there has been little sign that North Korea and the United States are any closer to narrowing differences on the nuclear issue.

US secretary of state Mike Pompeo told reporters shortly before departing to South Korea that a fresh round of talks will likely happen "sometime in July" and the North's negotiators would be foreign ministry diplomats.

Pompeo made clear in a tweet later that the United States believed that sanctions put in place under UN Security Council resolutions needed to remain in place as talks moved forward.

"We remain ready to engage (North Korea) in negotiations, but remain firm on the implementation of UNSCRs ahead of denuclearisation," he said.

The meeting, initiated by a spur-of-the-moment tweet by Trump that Kim said took him by surprise, once again displayed the rapport between the two. But they are no closer to narrowing the gap between their positions since they walked away from their summit in February in Vietnam.

The two men shook hands warmly and expressed hopes for peace when they met for the third time in just over a year on the old Cold War frontier that for decades has symbolised the hostility between their countries, which are technically still at war.

Trump, escorted by Kim, briefly crossed a military demarcation line into the North side of the Joint Security Area (JSA), patrolled by soldiers from both Koreas.

Moments later, they returned to the southern side and joined South Korea's President Moon Jae-in for a brief chat, marking an unprecedented three-way gathering.

Trump and Kim then held a closed-door meeting for nearly an hour.

"We just had a very, very good meeting," Trump said after the talks. "We'll see what can happen."

He said both sides would set up teams to push forward stalled talks aimed at getting North Korea to give up its nuclear weapons, adding "speed is not the thing."

Pope Francis, making his weekly address in St. Peter's Square, praised the meeting. "I salute the protagonists, with a prayer that such a significant gesture will be a further step on the road to peace, not only on that peninsula, but for the good of the entire world," he said.

Trump and Kim met for the first time in Singapore in June last year, and agreed to improve relations and work towards the denuclearisation of the Korean peninsula.

But the second summit in Hanoi broke down after the two sides failed to narrow differences between a US demand for North Korea to give up its nuclear weapons and a North Korean demand for sanctions relief.

North Korea has pursued nuclear and missile programmes for years in defiance of UN Security Council resolutions, and easing tensions with North Korea is one of the US president's top foreign policy priorities.

The DMZ was set up after the 1950-53 Korean War ended in an armistice, not a truce, leaving North Korea and the United States still technically at war.