U.S. President Donald Trump declared on Wednesday that 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 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'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.

And while Trump and Kim have signed a joint statement that contained a repeat of past promises to work toward a denuclearized Korean Peninsula, the details haven't been nailed down. Trump has said strong verification would be included in a final agreement, with the particulars sorted out by his team with the North Koreans next week.

"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!"

President George W. Bush's speech aboard the USS Abraham Lincoln in May 2003, complete with 'Mission Accomplished' banner, proved to be a premature assessment of the state of American combat operations in Iraq. (Larry Downing/Reuters)

That tweet failed to point out that while North Korea seriously ramped up its missile testing beginning in the last year of the Obama administration, its September 2017 test was seen as multiple times more powerful than previous launches. As well, Trump and Kim exchanged a bellicose series of insults and threats last year, raising fears of conflict.

Trump's chest-thumping tweets 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.

Democratic Sen. Charles Schumer and Richard Haaas, the Council on Foreign Relations think-tank head who previously served in four different administrations, were among several to quickly undercut Trump's claims.

Mr. President, if only it were that easy, that simple. <a href="https://t.co/zDMhHTkxCa">https://t.co/zDMhHTkxCa</a> —@SenSchumer

.<a href="https://twitter.com/realDonaldTrump?ref_src=twsrc%5Etfw">@realDonaldTrump</a> claim there is no longer a NK nuclear threat patently false. 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 —@RichardHaass

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

Pompeo looks to reassure allies

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

In Pyongyang, North Korean state media heralded claims of a victorious meeting with the U.S. 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.

There were worries, especially in Tokyo and Seoul, which have huge U.S. military presences, about Trump agreeing to halt U.S. 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 U.S.," said Lee Jae Sung, from Incheon. "I think they will be continued for a while."

Secretary of State Mike Pompeo said Wednesday the drills would resume if North Korea stopped negotiating in good faith.

Pompeo arrived at Osan Air Base south of Seoul from Singapore early Wednesday evening. He met for nearly an hour at the air base with Gen. Vincent Brooks, commander of U.S. Forces Korea, before heading by motorcade to Seoul.

There are some 28,500 American troops stationed in South Korea.

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.

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.