SINGAPORE (AP) — US President Donald Trump declared on Twitter Wednesday that there was “no longer a Nuclear Threat from North Korea,” a bold and questionable claim following his summit with leader Kim Jong Un that produced few guarantees on how and when Pyongyang would disarm.

“Just landed — a long trip, but everybody can now feel much safer than the day I took office,” he tweeted. “There is no longer a Nuclear Threat from North Korea. Meeting with Kim Jong Un was an interesting and very positive experience. North Korea has great potential for the future!”

Trump and Kim were returning to their respective strongholds following the talks — but to far different receptions.

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In Pyongyang, the North Korean autocrat woke up to state media’s enthusiastic claims of a victorious meeting with the US president; photos of him standing side-by-side with Trump on the world stage were splashed across newspapers. Trump, meanwhile, faced questions about whether he gave away too much in return for far too little when he bestowed a new legitimacy on Kim’s rule and agreed, at Pyongyang’s request, to end war games with Seoul that the allies had long portrayed as crucial to Asian safety.

As the top US diplomat jetted to South Korea for follow-up talks Wednesday, much of Asia was still trying to process the whirlwind events of the day before.

There was, at times, a surreal quality to the carefully staged, five-hour meeting of two men who’d been threatening each other with nuclear war and insulting each other’s mental and physical attributes just months before. Trump repeatedly praised Kim’s negotiating skills and their new relationship and expressed hope for “a bright new future” for Kim’s impoverished nation.

But there were worries, especially in Tokyo and Seoul, which both have huge US military presences, about Trump agreeing to halt US military exercises with South Korea, which the North has long claimed were invasion preparations. That concession to Kim appeared to catch the Pentagon and officials in Seoul off guard, and some South Koreans were alarmed.

“The United States is our ally, so the joint military drills are still necessary to maintain our relationship with the US,” said Lee Jae Sung, from Incheon. “I think they will be continued for a while.”

US Secretary of State Mike Pompeo arrived at Osan Air Base south of Seoul from Singapore early Wednesday evening. Pompeo met for close to an hour with Gen. Vincent Brooks, commander of US Forces Korea, at the air base before heading by motorcade to Seoul.

Pompeo will meet President Moon Jae-in on Thursday morning to discuss the summit. Japanese Foreign Minister Taro Kono is also heading to Seoul and is due to meet with Pompeo and his South Korean counterpart. Pompeo, the former CIA director, then plans to fly to Beijing to update the Chinese government on the talks.

On the issue the world has been most fixated on — North Korea’s pursuit of a nuclear arsenal meant to target the entire US mainland — Trump and Kim signed a joint statement that contained a repeat of past vows to work toward a denuclearized Korean Peninsula. The details of how and when the North would denuclearize appear yet to be determined, as are the nature of the unspecified “protections” Trump is pledging to Kim and his government.

Despite the confusion and disappointment among some, the summit managed to, for a time at least, reset a relationship that has long been characterized by bloodshed and threats. In agreeing to the summit, Trump risked granting Kim his long-sought recognition on the world stage in hopes of ending the North’s nuclear program.

“Before taking office people were assuming that we were going to War with North Korea,” Trump tweeted Wednesday. “President (Barack) Obama said that North Korea was our biggest and most dangerous problem. No longer — sleep well tonight!”

Trump’s claim that North Korea no longer poses a nuclear threat is questionable.

North Korea is believed to possess more than 50 nuclear warheads, with its atomic program spread across more than 100 sites constructed over decades to evade international inspections. Trump insisted that strong verification of denuclearization would be included in a final agreement, saying it was a detail his team would begin sorting out with the North Koreans next week.

Moon has championed engagement with the North, and the agreement’s language on North Korea’s nuclear program was similar to what the leaders of North and South Korea came up with at their own summit in April. Trump and Kim referred back to the so-called Panmunjom Declaration, which contained a weak commitment to denuclearization but no specifics on how to achieve it.

As Trump acknowledged that denuclearization would not be accomplished overnight, the North suggested Wednesday that Trump had moved away from his demand for complete denuclearization before US sanctions on the long-isolated country are removed.

The state-run Korean Central News Agency said the two leaders “shared recognition to the effect that it is important to abide by the principle of step-by-step and simultaneous action in achieving peace, stability and denuclearization of the Korean Peninsula.” KCNA also reported that Trump had expressed his intention to lift sanctions “over a period of goodwill dialogue” between the two countries.

The White House declined to comment on the North Korean characterization of the deal. Instead, officials merely pointed to the text of the joint Trump-Kim statement, and left it at that.

The Singapore agreement does not detail plans for North Korea to demolish a missile engine testing site, a concession Trump said he’d won, or Trump’s promise to end military exercises in the South while negotiations between the US and the North continue. Trump cast that decision as a cost-saving measure, but also called the exercises “inappropriate” while talks continue.

While progress on the nuclear question was murky, the leaders spent the public portions of their five hours together expressing optimism and making a show of their new relationship. Trump declared he and Kim had developed “a very special bond,” and seemed to delight in giving Kim a glimpse of the presidential limousine. Kim, for his part, said the leaders had “decided to leave the past behind” and promised, “The world will see a major change.”

The US has stationed combat troops in South Korea since the end of the Korean War in the 1950s and has used them in a variety of drills. The next scheduled major exercise, involving tens of thousands of troops, normally is held in August.

The Pentagon said Tuesday it was consulting with the White House and others, but was silent on whether the August exercise would proceed. Mattis’s chief spokeswoman, Dana W. White, told reporters he was “in full alignment” with Trump.

In Japan, the prospect of canceled US-South Korean drills was met with concern.

“The US-South Korea joint exercises and US forces in South Korea play significant roles for security in East Asia,” Japanese Defense Minister Itsunori Onodera told reporters Wednesday. He said he planned to continue sharing the view with Washington and Seoul.

Chief Cabinet Secretary Yoshihide Suga said Japan wants to get further explanations from the US and South Korea on the issue. He declined to comment further.

In South Korea, the liberal Kyunghyang Shinmun newspaper said Trump and Kim have started a “march of peace” to end nearly seven decades of hostility and pave the way for permanent peace and prosperity on the peninsula.

The conservative Chosun Ilbo, the country’s biggest paper, was decidedly more critical, denouncing Trump for offering the end of military drills while failing to convince the North to commit to verifiably giving up its nukes for good. It called the summit “dumbfounding and nonsensical,” and said it will allow North Korea to permanently maintain its nuclear weapons program.