WASHINGTON, United States (AFP) — A jubilant-sounding President Donald Trump declared Wednesday that his “deal” with Kim Jong Un has ended the North Korean nuclear threat, as his top diplomat said he hoped to see “major disarmament” of the country by 2020.

Despite the lack of detail, or binding terms in the joint statement agreed with Kim — which has alarmed a majority of observers of the nuclear standoff — Trump struck a resolutely bullish tone. “There is no longer a Nuclear Threat from North Korea,” he tweeted in one of a series of early morning pronouncements.

Trump added that everybody “can now feel much safer than the day I took office” and people could “sleep well tonight!”

Critics said the unprecedented encounter between Kim and Trump was more style than substance, producing a document short on specifics about the key issue of Pyongyang’s atomic weapons.

But the US president trumpeted the outcome as a “deal” with North Korea and vowed there would be “no more rocket launches, nuclear testing or research!”

Secretary of State Mike Pompeo, speaking to reporters in Seoul, said the United States hoped for “major disarmament” of North Korea by the end of 2020.

In the summit statement, Kim pledged to “work toward the complete denuclearisation of the Korean Peninsula” — a stock phrase favoured by Pyongyang that stopped short of longstanding US demands for North Korea to give up its atomic arsenal in a “verifiable” and “irreversible” way.

When questioned on the wording, Pompeo said Trump’s intention was to allow the US the opportunity to pursue further productive conversations on the issue with Pyongyang.

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

“One can’t completely denuclearize without validating, authenticating.”

Pompeo said he expects the US would next speak to North Korean officials “fairly quickly after we return to our home countries,” adding he was “very confident” that some form of engagement would occur in the next week.

In North Korea, state media praised Kim for “opening a new chapter” in relations with the US, and said Trump had accepted an invitation to visit the North.

Just months ago, Kim and Trump were trading threats and personal insults as the North conducted its sixth and most powerful nuclear test.

Adam Schiff, a top US Democrat and staunch Trump critic, warned the standoff was far from resolved.

“North Korea still has all its nuclear missiles, and we only got a vague promise of future denuclearisation from a regime that can’t be trusted. North Korea is a real and present threat. “So is a dangerously naive president,” Schiff said.

But Victor Cha, a former US pointman on North Korea, gave Trump more credit, writing in The New York Times: “Despite its many flaws, the Singapore summit represents the start of a diplomatic process that takes us away from the brink of war.”