WASHINGTON — President Trump and North Korea’s Kim Jong Un agreed Wednesday that their Singapore summit had been a momentous and unqualified success, but offered somewhat differing versions of what they had accomplished and where they go from here.

Trump, in tweets that began as Air Force One made an early-morning landing, declared America’s “biggest and most dangerous problem” all but resolved. The “deal” he struck with Kim, he said, meant there was “no longer a Nuclear Threat from North Korea,” and “everybody can now feel much safer.”

Secretary of State Mike Pompeo said the administration expected “major disarmament” by North Korea before the end of Trump’s first term.

Kim, or at least his country’s state-run news agency, said the two leaders had decided to end “extreme hostile relations” and described the beginning of a “step-by-step and simultaneous” process that would eventually lead to peace and “denuclearization of the Korean Peninsula.”

Both sides said Trump had agreed to halt military exercises with South Korea. Additionally, according to Pyongyang, the president offered “security guarantees … and [to] lift sanctions” as their dialogue proceeded, to which North Korea would respond with “additional good-will measures.”

Unlike Kim, whose government brooks no domestic disagreement or questions, Trump faced skepticism that one day of talks had achieved so much. His all-is-resolved description seemed to fly in the face of decades of hostility, unkept promises, and the widespread belief, shared by U.S. intelligence agencies, that North Korea would never give up the nuclear weapons it sought for so long.

The meeting clearly brought a step back from the brink of war, which Trump himself had threatened. Uneasiness in Washington stemmed largely from his lavish praise of Kim as “a very talented man” with a “great personality;” the choreographed, feel-good optics of the summit; and the striking lack of details in the brief declaration the two leaders signed.

Pompeo, visiting Seoul as part of a tour to brief regional governments on the summit, told reporters that questions about verification of North Korean denuclearization and its irreversibility – neither of which was mentioned in the document – were “insulting and ridiculous and frankly ludicrous.”

Referring to his own extensive pre-summit communications with North Korea and the meeting itself, Pompeo said he would not talk about “discussions between the two parties.” But he was confident, he said, that the North Koreans “understand what we’re prepared to do, and [the] handful of things we’re not likely to do.”

“Not all of that work appeared in the final document,” Pompeo said. “But lots of other places where there were understandings reached, we couldn’t reduce them to writing.” He said those understandings would provide a starting point when detailed negotiations begin.

Those talks, which he is to lead, would start “some time in the next week or so,” Pompeo said, and would be completed, “most definitely,” within the next two years. He said he had already assembled a strong negotiating team.

House Speaker Paul Ryan, R-Wis., said Trump deserved credit for taking a new approach on a foreign policy challenge that has bedeviled past presidents.

“The status quo was not working with North Korea,” Ryan told reporters on Capitol Hill. “The president should be applauded for disrupting the status quo.”

Ryan said that he is “encouraged” by continued negotiations on denuclearization led by Pompeo. At the same time, he said, there is no question that North Korea is a “terrible regime” and “we should be under no delusions that this will be fast.”

Some Republicans sounded more doubtful of those talks bearing fruit.

Sen. Marco Rubio, R-Fla., said it’s understandable for Trump to be optimistic because “he’s the guy negotiating.”

“He needs to make the other side feel like he’s serious about getting something done,” Rubio said. “But for the rest of us who are watching and know the history of North Korea, we should be skeptical. This is a country that’s made promises before and has broken them.”

Sen. Bob Corker, R-Tenn., said Tuesday that he wants Pompeo to brief senators on the substance of what the two nations discussed, including whether U.S. troops stationed on the Korean Peninsula would remain.

“I have no idea” whether Trump secured anything of substance, said Corker, the retiring chairman of the Senate Foreign Relations Committee. “At this juncture, I don’t think we know enough to challenge or celebrate.”

Democrats and some analysts were more directly negative in their assessments.

“What planet is the president on?” Senate Minority Leader Chuck Schumer, D-N.Y., said during remarks on the Senate floor. “Saying it doesn’t make it so. North Korea still has nuclear weapons. It still has ICBMs. It still has the United States in danger. Somehow President Trump thinks when he says something it becomes reality, if it were only that easy, only that simple.”

Sen. Chris Van Hollen, D-Md., meanwhile, said on Twitter that Trump was being “truly delusional,” noting that North Korea has “the same arsenal today as 48 hours ago.”

Rep. Adam Schiff, D-Calif., also mocked Trump, saying on Twitter: “One trip and it’s ‘mission accomplished,’ Mr. President?”

“North Korea is a real and present threat,” Schiff said. “So is a dangerously naive president.”

Richard Haass, the president of the Council on Foreign Relations, said “the summit changed nothing.”

“Worse yet, overselling the summit makes it harder to keep sanctions in place, further reducing pressure on NK to reduce (much less give up) its nuclear weapons and missiles,” Haass said on Twitter.

Trump, in tweets that continued well after his arrival at the White House Wednesday morning, defended his decision to halt military exercises, saying that “We save a fortune by not doing war games, as long as we are negotiating in good faith – which both sides are!”

He called his meeting with Kim “an interesting and very positive experience.”

He also said that before he took office last year, “people were assuming that we were going to War with North Korea.”

“President Obama said that North Korea was our biggest and most dangerous problem. No longer – sleep well tonight!” the president wrote.

Trump, who has frequently sparred with the media, was also unsparing in his criticism of television coverage of the summit, pointing out two networks for scorn.

“So funny to watch the Fake News, especially NBC and CNN,” he said on Twitter. “They are fighting hard to downplay the deal with North Korea. 500 days ago they would have ‘begged’ for this deal-looked like war would break out. Our Country’s biggest enemy is the Fake News so easily promulgated by fools!”

Appearing on Fox News on Wednesday, White House counselor Kellyanne Conway stoked earlier talk among Trump supporters that his efforts on North Korea would deserve a Nobel Peace Prize.

“Look, the last president was handed the Nobel Peace Prize – this president’s actually going to earn it and that’s all we need to know from this,” Conway said.

Obama won the prize in 2009 for his efforts to strengthen international diplomacy.

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