South Korean President Moon Jae-in expressed confidence on Monday that the United States and North Korea will eventually reach an agreement on denuclearization, telling his top security officials to find ways to help narrow the gap between the two sides.

"I believe the North Korea-US negotiations will reach an agreement in the end, but I ask you to work for an early resumption of working-level dialogue between the two because we do not want the stalemate to be prolonged," the president said in a National Security Council meeting held at his office Cheong Wa Dae in Seoul.

The NSC meeting was the first to be chaired by the president in nearly nine months.

It came four days after the second meeting between US President Donald Trump and North Korean leader Kim Jong-un failed to reach an agreement.

In a press conference shortly after their meeting in Hanoi, Trump said the North demanded all US and international sanctions be lifted in their entirety but only offered to give up its well-known nuclear facilities in Yongbyon.

The US president made it clear that there are more nuclear facilities or weapons the North must dismantle to reach complete denuclearization.

Moon said the second Trump-Kim meeting in Hanoi was still a success.

"The second North Korea-US summit, though it is very disappointing in its result, was a chance to confirm the very meaningful progress that has been made through dialogue between the two countries," he said, according to Cheong Wa Dae pool reports.

Moon also stressed that the fact both Washington and Pyongyang have refrained from escalating tension, even after their failure to reach an agreement, suggested the possibility of progress in the future.

The South Korean president noted the summit hinted at the prospect of permanently shutting down the Yongbyon facilities, which he said would mean the North's denuclearization process entering a phase of no-return.

"First, complete shutdown of the Yongbyon nuclear facilities was discussed. Permanently dismantling the Yongbyon facilities, which are the backbone of North Korea's nuclear program, under the observation and inspection of the United States has come into view," he said.

"Should the Yongbyon nuclear facilities that include plutonium reprocessing facilities and uranium enrichment facilities be fully and completely dismantled, North Korea's denuclearization process could be said to have entered an irreversible stage," the president added.

To this end, Moon told his top security officials to seek ways to narrow the difference between the US and North Korea.

"First, I ask you to accurately identify the difference that prevented the two sides from reaching an agreement at the latest North Korea-US summit and find ways to narrow that difference," he said.

The president noted one way to promote future dialogue may be improving his country's own relations with the communist North.

"Second, I ask you to actively find ways to assist North Korea-US dialogue by developing inter-Korean relations within the boundaries of sanctions. In addition, I ask you to prepare for (the start) of inter-Korean cooperation projects that were reached under the Panmunjom declaration and Pyongyang declaration," Moon said.

The South Korean president has held three bilateral summits with the North Korean leader, with the latest meeting held in the North Korean capital in September.

"We hope the two countries will continue their dialogue and that their two leaders will meet again in the near future and reach the agreement that they failed to reach this time," Moon told the NSC meeting. (Yonhap)