Trump said Thursday Kim demanded the lifting of sanctions on Pyongyang "in their entirety." The president said he walked away from the talks, as it was not appropriate to accept Kim's demand for denuclearization measures related to the Yongbyon nuclear complex alone. Trump talked about other nuclear activities under way including an "uranium enrichment" program.

It remained unclear which side is telling the truth.

The North Korean minister said his country offered to "permanently" get rid of plutonium and uranium processing facilities in Yongbyon under the monitoring of US experts if sanctions against his regime were partially removed.

 That represents Pyongyang's best denuclearization offer at the moment, given the current level of mutual confidence, he added.

Among a total of 11 UN Security Council sanctions resolutions, Ri said, Pyongyang wants only five, adopted between 2016-2017, to be removed first as they hamper the livelihood of the people.

What has become clear through this week's Hanoi summit, he added, is that Washington is not ready to accept Pyongyang's proposal, which won't change even in possible future negotiations.

After Ri's statement, Vice Foreign Minister Choe Son-hui told reporters that she has an impression that Kim Jong-un might have lost his appetite for bargaining with Trump due to his negative response.

She added there's no schedule fixed yet on additional talks with Washington.

On Thursday, the second summit between Trump and Kim finished abruptly with no agreement signed.

It cast further gloom over the already troubled denuclearization and peace-building processes and the months of bromance between the leaders.

Trump, however, left the door open for continued dialogue, claiming his relationship with Kim remains strong.

"It was about sanctions," Trump said at a press conference just before his departure from Hanoi. "Basically, they wanted the sanctions lifted in their entirety, but we couldn't do that."

He added there was a gap between what Washington and Pyongyang wanted.

"They wanted sanctions lifted but they weren't willing to do an area we wanted. They were willing to give us areas but not the ones we wanted," he said.

Trump said that the issue of dismantling the North's Yongbyon facilities, arguably the most crucial element in its nuclear development, was discussed in the summit, their first in eight months, but it was "not enough."

"We had to have more than that. But he just wants all the sanctions off first," he said, adding his administration has information on other secret weapons development, including a "uranium-enrichment plan," that has not been reported by media.

"I think they were surprised we knew," Trump said.

Asked if he agreed with Kim on a third summit, Trump said, "No we haven't ... we'll see if it happens."

He argued, however, that the Hanoi talks were not without progress, citing Kim's promise to continue the suspension of nuclear and missile testing. He earlier said the Hanoi session won't be his last meeting with Kim, as he's "in no rush" for a nuclear deal.

Standing next to Trump and speaking to reporters, Secretary of State Mike Pompeo also said that the failure to reach a deal in Hanoi does not necessarily mean the denuclearization process has hit a dead end.

"I am still optimistic," he said, and expressed hope that Pyongyang and Washington will resume working-level negotiations "in the days and weeks ahead" to resolve the "very complex problem" associated with timing and sequencing issues.

In his phone talks with Trump, South Korean President Moon Jae-in expressed hope that dialogue will go on, according to his office, Cheong Wa Dae.

On his way back to Washington, DC, on Air Force One, Trump was quoted as asking Moon to play an "active mediating role."

Moon said his government will provide necessary support for follow-up talks between Pyongyang and Washington to bear fruit.

The liberal president is credited with having played a leading role in creating the high-profile diplomatic process.

Nonetheless, the failure to yield a Hanoi declaration has cast further doubts over the already-troubled denuclearization and peace-building efforts.

It also demonstrated the high risk of a "top-down" approach to deal with the issue, with an ultimate resolution elusive for decades.

China urged both sides to make concessions to "meet each other halfway" to keep the "hard-won" process rolling.

The situation in the Korean Peninsula experienced a significant turnaround over the past year and it is worth continuing, the foreign ministry spokesman, Lu Kang, said at a regular press briefing in Beijing.

Trump and Kim started their Hanoi summit Wednesday in a seemingly amicable atmosphere.

Before noon Thursday, they even talked positively about the establishment of a US liaison office in Pyongyang, although Trump reiterated that he was "in no hurry" for a nuclear deal.

At the start of an expanded meeting, the North Korean leader told a pool reporter that he was discussing "concrete denuclearization measures" in this week's bargaining.

"If I weren't willing to do that, I wouldn't be here right now," Kim said in response to a question about whether he's ready to denuclearize.

The positive mood changed to skepticism about a deal with news that the leaders cut short their summit.

They called off a joint working dinner and an agreement signing ceremony.

Trump abruptly moved up his press conference by two hours.

Then, Trump's office released a brief statement.

"No agreement was reached at this time, but their respective teams look forward to meeting in the future," White House press secretary Sarah Sanders said in a statement.

It added, "The two leaders discussed various ways to advance denuclearization and economic-driven concepts."

Trump is expected to face harsher criticism of his diplomacy on Pyongyang from political opponents in Washington.

 South Korea's push for closer inter-Korean economic cooperation is likely to suffer a heavy setback.

Kim will have to rethink his strategy, as the voice of hard-line military officials at home may ring louder.

On the future of combined military drills with South Korea, meanwhile, Trump questioned whether they are necessary. He cited the huge costs for related operations, including the dispatch of high-tech "strategic assets" to Korea, saying South Korea should provide more financial contributions.

"We spend hundreds of millions of dollars on those exercises, and I hated to see it," he said. "And frankly, I was sort of the opinion that South Korea should help us with that."

In spite of his unsuccessful nuclear negotiations in Hanoi, Kim plans to start a two-day working, goodwill visit to Vietnam on Friday as planned, the Vietnamese government said, without specifying his schedule. (Yonhap)