WASHINGTON — As President Trump declared his summit with Kim Jong Un a smashing success, Secretary of State Mike Pompeo quickly began the hard part: negotiating the complex details for a deal to eliminate North Korea’s nuclear threat.

Pompeo went straight to Seoul after the Singapore summit to confer Wednesday with South Korean allies and top U.S. military commanders in the region. He said that dismantling North Korea’s nuclear arsenal could take 2½ years, the most concrete time frame ascribed to what would undoubtedly be a long process.

Pompeo also had to explain to both the allies and American commanders the unexpected announcement from Trump in Singapore that he is halting annual joint U.S.-South Korea military exercises, which the president described as provocative war games, using the lexicon of North Korea and China. Allies, including in Japan, were blindsided by the decision, which triggered sharp criticism from Congress, including Republicans, and from former and current U.S. officials.

Pompeo met with Gen. Vincent Brooks, the top U.S. commander in South Korea, in what was billed as a brief greeting but stretched into nearly an hourlong closed-door discussion.

On Thursday, he is to meet with South Korean President Moon Jae-in, a principal force behind arranging the Singapore summit, and with the foreign ministers of South Korea and Japan. Later he continues to Beijing, where Chinese officials are thought to be extremely pleased with the summit results, but vexed by ongoing trade disputes with Washington.

Complicating Pompeo’s diplomatic work, Trump, upon his predawn arrival in Washington from Singapore, made the kind of “mission accomplished” proclamation that often comes back to haunt leaders. He declared on Twitter that “there is no longer a Nuclear Threat from North Korea.”

“A long trip, but everybody can now feel much safer than the day I took office,” he added.

“This is absolutely untrue,” said Nicholas Burns, a career diplomat and senior official under Presidents Clinton and George W. Bush. “North Korea is still a nuclear threat to the U.S., South Korea and Japan. Kim has not dismantled any part of his nuclear apparatus.”

Trump’s boast is at best premature. For now, Kim is likely to remain restrained about further nuclear and ballistic-missile testing. Yet despite Trump and Kim’s step away from what seemed last year to be the brink of nuclear war — tensions inflamed in part by Trump’s bellicose tweets and name-calling — Kim has as many nuclear warheads now as last week, and more than when Trump took office.

Another wrinkle: Official North Korean media are providing a different interpretation of what happened.

The tightly controlled press accounts in Pyongyang said Trump and Kim agreed that work “toward” denuclearization would involve “step-by-step and simultaneous action.” The reports suggested the Trump administration would lift key economic sanctions in the process, which was not mentioned in the leaders’ concluding joint statement.

They also said that denuclearization would occur in the southern half of the Korean peninsula as well as the north — in other words, it would entail ending the United States’ longtime nuclear presence, something American officials have said was off the table.

Trump and Kim held part of their meetings without aides or note-takers, only translators, so there is no record or confirmation of what was said.

Further, the vaguely worded final statement contained no detailed plan or timeline for nuclear disarmament, or even a definition of the process. Missing were the words that had become the administration’s mantra to describe its goal: “complete, verifiable and irreversible denuclearization.”

Pompeo, speaking to journalists traveling with him in Seoul, defended the lack of details and vagueness of the document. When a reporter asked why nothing was included on the crucial element of verification, Pompeo bristled and said the question was “insulting and ridiculous and, frankly, ludicrous.”

“Let me assure you that the ‘complete’ [denuclearization] encompasses ‘verifiable’ in the minds of everyone concerned,” he said.

“I am confident that they understand what we’re prepared to do, a handful of things we’re likely not prepared to do,” he added. “I am equally confident they understand that there will be in-depth verification.”

Pompeo said preparations before the summit produced many “understandings” that negotiating teams “couldn’t reduce to writing” in the final statement.

Just a day before the summit, Pompeo had said that “complete, verifiable and irreversible denuclearization” was the United States’ objective, as it has been for decades. “Verifiable” and “irreversible” do not appear in the document signed by Trump and Kim.

Asked if “major disarmament” could be accomplished by the end of Trump’s term, Pompeo said, “Absolutely.”

“We’re hopeful that we can achieve that in the next — what is it? — 2½ years, something like that,” he said. “We’re hopeful we get it done. There’s a lot of work left to do.”

In the leaders’ triumphant remarks, both Kim, through state media, and Trump, through Twitter, sought to put the best spin on a high-stakes summit that each leader is trying to sell to his public as not only a historic result but also a personal victory.

For Trump, one aim is to cast it as a major breakthrough to benefit Republican candidates in the midterm election — a goal already under discussion among political advisors.

That plan hinges on the summit imagery, including the leaders’ handshakes and backdrops of both nations’ flags — stagecraft that may matter more to many voters than questions about disarmament details, said a lobbyist in close contact with the White House.

“The American people believe Trump before they believe some member of Congress who has questions about the military exercises or some other thing,” the source said, speaking anonymously to be able to discuss administration thinking candidly.

“Unless Kim does something provocative, Trump wins,” the lobbyist added. “All they [Trump supporters] know is there was a guy in North Korea shooting off missiles, and now he’s not shooting missiles anymore.”

Overselling the fledgling deal for short-term political value, however, risks undercutting diplomacy and could make Pompeo’s job of forging a more durable and detailed disarmament plan all the more difficult.

Some analysts and diplomats warned that exaggerating progress this early could ease the pressure on North Korea to conform with international norms, and make it more difficult to hold together an alliance enforcing economic sanctions.

tracy.wilkinson@latimes.com

Stokols is a special correspondent.