By Joyce Lee

SEOUL (Reuters) – North Korean leader Kim Jong Un and U.S. President Donald Trump agreed at their meeting on Sunday to push forward dialogue for making a new breakthrough in the denuclearization of the Korean peninsula, North Korean state media said on Monday.

Trump became the first sitting U.S. president to set foot in North Korea on Sunday when he met Kim in the Demilitarized Zone (DMZ) between the two Koreas and agreed to resume stalled nuclear talks.

U.S. President Donald Trump shakes hands with North Korean leader Kim Jong Un as they meet at the demilitarized zone separating the two Koreas, in Panmunjom, South Korea, June 30, 2019. KCNA via REUTERS

“The top leaders of the two countries agreed to keep in close touch in the future, too, and resume and push forward productive dialogues for making a new breakthrough in the denuclearization of the Korean peninsula and in the bilateral relations,” KCNA news agency said.

The meeting, initiated by a tweet by Trump that Kim said took him by surprise, displayed the rapport between the two, but analysts said they were no closer to narrowing the gap between their positions since they walked away from their summit in February in Vietnam.

U.S. Secretary of State Mike Pompeo told reporters shortly before departing South Korea that a new round of talks would likely happen “sometime in July” and the North’s negotiators would be foreign ministry diplomats.

In a photo released by KCNA on Monday, North Korean Foreign Minister Ri Yong Ho and Pompeo are shown sitting next to Kim and Trump respectively in Freedom House, the building in which the two leaders had their one-on-one talks.

KCNA said that during the chat between Trump and Kim, the two leaders explained “issues of easing tensions on the Korean peninsula,” “issues of mutual concern and interest which become a stumbling block in solving those issues,” and “voiced full understanding and sympathy.”

Kim said it was the good personal relationship he had with Trump that made such a dramatic meeting possible at just one day’s notice and that the relationship with Trump would continue to produce good results, according to KCNA.

The two leaders’ “bold, brave decision” that led to the historic meeting “created unprecedented trust between the two countries” that had been tangled in deeply rooted animosity, KCNA said.

U.N. Secretary-General Antonio Guterres welcomed the meeting between Trump and Kim and “fully supports the continued efforts of the parties to establish new relations toward sustainable peace, security and complete and verifiable denuclearization of the Korean Peninsula”, U.N. spokesman Stephane Dujarric said in a statement.

China also welcomed the meeting, with a foreign ministry spokesman describing it as “constructive and achieving positive results”.

U.S. President Donald Trump shakes hands with North Korean leader Kim Jong Un as they meet at the demilitarized zone separating the two Koreas, in Panmunjom, South Korea, June 30, 2019. KCNA via REUTERS

But problems could lie ahead.

“The fact that the nuclear talks have jump-started is very encouraging, but that doesn’t mean that the two sides have already adjusted their positions and set the conditions for successful working-level negotiations,” said Kim Hyun-wook, a professor at the Korea National Diplomatic Academy.

Trump’s national security adviser, John Bolton, dismissed a report in The New York Times on Monday that Washington is seeking to soften its approach, floating an idea of accepting a nuclear freeze – instead of complete dismantlement – and giving tacit recognition that North Korea is a nuclear state.

“I read this NYT story with curiosity,” Bolton said in a tweet. “Neither the [National Security Council] staff nor I have discussed or heard of any desire to ‘settle for a nuclear freeze by NK.’ This was a reprehensible attempt by someone to box in the President. There should be consequences.”

(Reporting by Jack Kim and Joyce Lee; Additional reporting by Michelle Nichols at United Nations, Josh Smith in Seoul, and Ben Blanchard in Beijing; Editing by Peter Cooney and Sandra Maler)