WASHINGTON >> President Donald Trump declared today there was “no longer a Nuclear Threat from North Korea,” a dubious claim following his summit with leader Kim Jong Un that produced no guarantees on how or when Pyongyang would disarm.

Tempering Trump’s very upbeat assessment, his top diplomat, Mike Pompeo, cautioned that the U.S. would resume “war games” with close ally South Korea if the North stops negotiating in good faith. The president had announced a halt in the drills after his meeting with Kim on Tuesday.

The summit in Singapore, which marked a major reduction in tensions, yielded a joint statement that contained a promise to work toward a denuclearized Korean Peninsula, but it lacked details. That didn’t stop the president from talking up the outcome of what was the first meeting between a U.S. and North Korean leader in six decades of hostility. The Korean War ended in 1953 without a peace treaty, leaving the two sides in a technical state of war.

“Just landed – a long trip, but everybody can now feel much safer than the day I took office,” Trump tweeted early today. “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!”

Pompeo, who flew to Seoul to brief South Korean leaders on the summit, said the U.S. wants North Korea to take “major” nuclear disarmament steps within the next two years — before the end of Trump’s first term in 2021. He said the North Korean leader understands that “there will be in-depth verification” of nuclear commitments in any deal with the U.S.

While Trump was facing questions at home and among allies about whether he gave away too much in return for far too little at the summit, North Korean state media heralded claims of a victorious meeting with the U.S. president; photos of Kim standing side-by-side with Trump on the world stage were splashed across newspapers.

Trump’s own chest-thumping tweet seemed reminiscent of the “Mission Accomplished” banner flown behind President George W. Bush in 2003 when he spoke aboard a Navy ship following the U.S. invasion of Iraq. The words came back to haunt the administration, as the war dragged on throughout Bush’s presidency.

Trump’s claim that North Korea no longer poses a nuclear threat is questionable considering Pyongyang’s significant weapons arsenal.

Independent experts say the North could have enough fissile material for anywhere between about a dozen and 60 nuclear bombs. Last year it tested long-range missiles that could reach the U.S. mainland, although it remains unclear if it has mastered the technology to deliver a nuclear warhead that could re-enter the atmosphere and hit its target.

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

When asked whether Trump was jumping the gun by declaring victory, White House counselor Kellyanne Conway told reporters: “This president wants North Korea to completely denuclearize so obviously that has to be complete, verifiable and irreversible.

Freezing the regular military exercises with South Korea is a major concession to North Korea that has long claimed the drills were invasion preparations. It appeared to catch the Pentagon and officials in Seoul off guard, and some South Koreans were alarmed. Trump cast the decision as a cost-saving measure, but also called the exercises “inappropriate” while talks continue.

Pompeo said he was there when Trump talked about it with Kim, and the president “made very clear” that the condition for the freeze was that good-faith talks be ongoing. He told reporters that if the U.S. concludes they no longer are, the freeze “will no longer be in effect.”

“He was unambiguous about that and how he communicated it, both at the press conference but certainly when he was with Chairman Kim as well,” Pompeo said.

In North Korea today, Pyongyang’s first reports on the summit stressed to the nation’s people that Trump had agreed at Kim’s demand to halt the military exercises and suggested that Trump also said he would lift sanctions as negations progressed.

“President Trump appreciated that an atmosphere of peace and stability was created on the Korean Peninsula and in the region, although distressed with the extreme danger of armed clash only a few months ago, thanks to the proactive peace-loving measures taken by the respected Supreme Leader from the outset of this year,” the North’s state-run Korean Central News Agency said in a summary of the meeting.

Pompeo, after landing in South Korea, met for nearly an hour with Gen. Vincent Brooks, commander of U.S. Forces Korea. The secretary of state is to 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.

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

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

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