US president Donald Trump has declared on Twitter that there is “no longer a Nuclear Threat from North Korea” following his ground-breaking summit with Kim Jong Un.

Mr Trump’s claim comes despite few guarantees emerging from the Singapore meeting with the North Korean leader on how and when Pyongyang would disarm.

The American president 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!”

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

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 Mr Trump on the world stage were splashed across newspapers.

Mr Trump, meanwhile, faced questions about whether he gave away too much in return for far too little when he bestowed a new legitimacy on Mr Kim’s rule and agreed, at Pyongyang’s request, to end military exercises 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 on 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 between two men who had been threatening each other with nuclear war and insulting each other’s mental and physical attributes just months before.

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

Mike Pompeo and General Vincent Brooks
US secretary of state Mike Pompeo and US General Vincent K Brooks (AP)

But there are worries, especially in Tokyo and Seoul, which both have huge US military presences, about Mr Trump agreeing to halt US military exercises with South Korea, which the North has long claimed were invasion preparations.

That concession to Mr Kim appeared to catch the Pentagon and officials in Seoul off guard, and some South Koreans were alarmed.

US secretary of state Mike Pompeo met General Vincent Brooks, commander of US Forces Korea, after arriving in Seoul.

Mr Pompeo will meet South Korean 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 Mr Pompeo and his South Korean counterpart. Mr Pompeo, the former CIA director, then plans to fly to Beijing to update the Chinese government on the talks.

News coverage of the Singapore summit
People watch the news broadcast on the Singapore summit (AP)

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 – Mr Trump and Mr Kim signed a joint statement that contained a repeat of past vows to work toward a denuclearised Korean Peninsula.

The details of how and when the North would denuclearise appear yet to be determined, as are the nature of the unspecified “protections” Mr Trump is pledging to Mr Kim and his government.

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.

Mr 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 Mr Trump said he had won, nor Mr 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.