US president Donald Trump has declared there is “no longer a nuclear threat from North Korea” following his ground-breaking summit with Kim Jong Un in Singapore.

While no guarantees were produced at the summit over how or when Pyongyang would disarm, US secretary of state Mike Pompeo warned that the US would resume military exercises with South Korea if the North stops negotiating in good faith.

This came after Trump announced a halt in the drills after his meeting with North Korean leader Kim.

Pompeo also said the US wants North Korea to take “major” nuclear disarmament steps before the end of Trump’s first term in 2021.

The summit in Singapore, which marked a major reduction in tensions, yielded a joint statement that contained a promise to work toward a denuclearised Korean Peninsula, but it lacked details.

This did not stop the US president from talking up the outcome of what was the first meeting between a US 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.

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

“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!”

However, Pompeo, who flew to Seoul to brief South Korean leaders on the summit, said the North Korean leader understands that “there will be in-depth verification” of nuclear commitments in any deal with the US.

While the US leader 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 US president. Images of Mr Kim standing side-by-side with Trump on the world stage were splashed across newspapers.

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

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 US mainland, although it remains unclear if the regime has mastered the technology to deliver a nuclear warhead that could re-enter the atmosphere and hit its target.

North Korea is believed to possess more than 50 nuclear warheads, with its atomic programme spread across more than 100 sites constructed over decades to evade international inspections.

Trump insisted that strong verification of denuclearisation would be included in a final agreement, saying it was a detail his team would begin sorting out with the North Koreans next week.

The Singapore agreement does not detail plans for North Korea to demolish a missile engine testing site, a concession Trump said he had won.

There was also no mention of Trump’s promise to end military exercises in the South while negotiations between the US and the North continue. The US president cast that decision as a cost-saving measure, but also called the exercises “inappropriate” while talks continue.

Trump repeatedly praised Kim’s negotiating skills and their new relationship, and expressed hope for “a bright new future” for Kim’s impoverished nation.