North Korean leader Kim Jong Un and U.S. President Donald Trump separately expressed willingness over the weekend to meet June 12 in Singapore as originally planned, after days of conflicting signals from both sides.

Kim, in a summit Saturday with South Korean President Moon Jae In, voiced his "fixed will" to proceed with the first-ever North Korea-U.S. summit as initially scheduled, North Korea's state media reported Sunday.

Trump, who had canceled the summit on Thursday only to suggest it might still take place, told reporters at the White House on Saturday that arrangements appear to be "going along very well."

"We're looking at June 12 in Singapore, That hasn't changed," he said, speaking after it was announced that a team of U.S. officials would soon leave for Singapore to prepare for the possible summit.

The South and North Korean leaders held their surprise meeting -- the second in a month -- at the truce village of Panmunjeom after Trump revived hopes of a historic summit.

They held "in-depth" discussions on issues related to denuclearization and regional peace, while agreeing to hold high-level talks between officials of the two Koreas on June 1, the North's official Korean Central News Agency said.

Moon and Kim also shared the view that both countries should "exert joint efforts" to implement "at an early date" the declaration issued after their first meeting on April 27, KCNA said.

They reached a "satisfactory consensus" in the matters discussed at their talks, it said.

Kim told Moon that the two Koreas should "positively cooperate with each other" to improve Washington-Pyongyang relations, while he thanked him for his efforts to bring to fruition "the summit scheduled for June 12."

Moon told a press conference Sunday he hopes the upcoming preparatory meeting between U.S. and North Korean officials will go smoothly to ensure the summit's success in terms of denuclearization of the Korean Peninsula.

He said he hopes that a trilateral summit between two Koreas and the United States could take place if Trump-Kim talks are successful.

"I am expecting that we can make progress for the declaration" of the end of the 1950-1953 Korean War "through trilateral summit talks," he said.

Moon said his latest meeting with Kim was held at North Korea's request.

At their April 27 summit, the first between the two Koreas in over a decade, Kim and Moon issued the Panmunjeom Declaration calling for "complete" denuclearization of the Korean Peninsula as well as efforts to declare a formal end to the war.

In the Korean War, U.S.-led multilateral forces fought alongside South Korea against the North, which was supported by China and the Soviet Union. Hostilities ceased with an armistice agreement signed on July 27, 1953 by the U.N. Command, North Korea and China.

China, Pyongyang's close ally, has also called on the United States and North Korea to hold their summit to that same end.

Beijing-Pyongyang relations have been drastically improving recently in the wake of Kim's visit to China in March, on his first foreign trip since becoming the supreme leader following the death of his father Kim Jong Il in December 2011.

Kim has tried to bolster ties with Chinese President Xi Jinping ahead of envisioned tough negotiations with Trump.

Moon, who has pledged to serve as a broker between Pyongyang and Washington in talks over a potential U.S.-North Korea summit, met with Trump last Tuesday in Washington to discuss issues related to the divided peninsula.

But just two days later, Trump canceled his summit with Kim in a move that left Moon "very perplexed."

North Korea, in a surprisingly conciliatory statement Friday, urged Trump to reconsider his decision, prompting him to reverse course.

That statement from First Vice Foreign Minister Kim Kye Gwan, Pyongyang's long-serving point man on nuclear issues, was in marked contrast with the belligerent rhetoric issue by him and another senior Foreign Ministry official earlier this month

"We would like to make known to the U.S. side once again that we have the intent to sit with the U.S. side to solve problem regardless of ways at any time," he said, according to KCNA.

Kim is believed to be keen to ask the United States to accept the continuation of North Korea's hereditary regime, in return for Pyongyang vowing to denuclearize in a "phased" and "synchronized" manner.

Trump, however, has put pressure on North Korea to abandon all its nuclear weapons as soon as possible if Pyongyang wants to receive returns.