SEOUL — The leader of North Korea, Kim Jong Un, said during a surprise summit meeting that he is determined to meet President Trump and discuss a “complete denuclearization of the Korean Peninsula,’’ South Korean President Moon Jae-in said Sunday.

Kim met unexpectedly with Moon on Saturday to discuss salvaging a canceled summit meeting between Kim and Trump, a new twist in the whirlwind of diplomacy over the fate of the North’s nuclear arsenal. The leaders of the two Koreas met for two hours on the North Korean side of Panmunjom, a “truce village’’ inside the Demilitarized Zone that separates the two Koreas.

Moon gave the first details of Saturday’s meeting in a news conference held Sunday morning in Seoul, the South Korean capital. He said that during the meeting, Kim expressed a desire to “end a history of war and confrontation’’ on the peninsula. Kim also said he was willing to talk about getting rid of North Korea’s nuclear weapons, a topic the Trump administration has said was a precondition for a meeting.

Moon said Kim told him he wanted to go though with his planned summit meeting with Trump and to make it a success. The Trump-Kim meeting, which would be the first between the heads of state of the United States and North Korea, had been scheduled for June 12 in Singapore but was abruptly canceled Thursday by Trump.

Trump said he was pulling out of the meeting, citing “tremendous anger and open hostility’’ from North Korea. But a day later, the US president said he was reconsidering.

On Sunday, Moon said it was Kim who proposed the second summit meeting between them, suggesting that the young North Korean dictator is keen for the landmark meeting with Trump to take place.

During their time together, Moon said he briefed Kim on his meeting with Trump in Washington last week, telling the North Korean leader that the United States was willing to end hostile relations and provide economic cooperation with North Korea should it completely denuclearize.

“Since both Chairman Kim and President Trump want a successful summit, I stressed that the two sides need to communicate directly to remove their misunderstandings and to hold sufficient working-level talks on the agenda for the summit meeting,’’ Moon said.

“Chairman Kim agreed,’’ he added.

It was the second meeting in a month by Moon and Kim, with the first on the South Korean side of Panmunjom on April 27. The second meeting was held in secret and announced only after it took place.

At Saturday’s meeting, Kim thanked the South Korean president for his efforts to bring about the summit “and expressed his fixed will on the historic DPRK-US summit talks,’’ the North’s official Korean Central News Agency reported, using the abbreviation for the country’s official name, the Democratic People’s Republic of Korea.

The report by the news agency marked the first time North Korea formally acknowledged there was a plan for Kim to meet Trump on June 12, and it also appeared to confirm Kim’s desire to negotiate face-to-face with the US leader.

Moon’s government has worked for months to help set up the first meeting between the leaders of North Korea and the United States, where it hoped Kim and Trump would resolve the dispute over the North’s nuclear weapons program.

Trump’s sudden cancellation of the meeting at first appeared to be a blow to Moon, who had staked much on brokering it. But the announcement by Trump set off a head-spinning series of diplomatic maneuvers aimed at saving the meeting.

North Korea responded to Trump’s decision with a surprisingly conciliatory gesture, asking Trump to reconsider and saying the North was ready to resume dialogue.

On Friday, Trump said his administration was back in touch with North Korea and the two sides may reschedule the meeting with Kim, perhaps even on the June 12 date.

“We’ll see what happens,’’ Trump said. “We’d like to do it. We’ll see what happens.’’

For weeks, Trump had issued a steady stream of enthusiastic comments and Twitter posts on his planned summit with Kim, although he also warned it might not happen.

Signs of trouble emerged last week, when North Korea issued two angry statements. North Korea first pulled out of planned high-level talks with South Korea, protesting a joint military exercise between the South and the United States.

It also warned that if Washington continued to insist on a “unilateral’’ abandonment of its nuclear arsenal, it would “no longer be interested’’ in a summit with Trump. The North focused its anger on Trump’s hard-line national security adviser, John R. Bolton, who has demanded that North Korea dismantle its nuclear arsenal before expecting reciprocal measures from Washington.

When US officials arrived in Singapore last week for working-level talks with the North Korean counterparts to prepare for the summit, the North Koreans stood them up, according to White House officials.

Then in an interview this week, Vice President Mike Pence repeated Bolton’s demand. On Thursday, North Korea called Pence a “political dummy’’ and warned of a “nuclear-to-nuclear showdown’’ with the United States.