Donald Trump has told the world it can "sleep well tonight" after landing back in the US following his summit with Kim Jong Un.

The US president says everyone can feel much safer now that he has signed a historic document with the North Korean leader to promote peace.

Mr Trump wrote on Twitter following their summit in Singapore on Tuesday: "Just landed – a long trip, but everybody can now feel much safer than the day I took office.

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!

— Donald J. Trump (@realDonaldTrump) June 13, 2018

"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!

"Before taking office people were assuming that we were going to war with North Korea.

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

— Donald J. Trump (@realDonaldTrump) June 13, 2018

"President Obama said that North Korea was our biggest and most dangerous problem. No longer – sleep well tonight!"

US Secretary of State Mike Pompeo has landed at Osan Air Base south of Seoul and is due to have meetings with America's allies in the aftermath of the summit.

Image: Mr Trump tweeted that North Korea was no longer a threat

He is expected to meet privately in the evening with General Vincent Brooks, commander of US Forces Korea.

Mr Pompeo will meet President Moon Jae-in on Thursday morning to discuss the summit.

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Japanese Foreign Minister Taro Kono is also heading to Seoul and is due to meet Mr Pompeo and his South Korean counterpart.

Mr Pompeo will then fly to Beijing to update the Chinese government on the talks.

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A spokesman of South Korean President Moon Jae-in said Washington and Seoul needed to consider a "variety of ways to further facilitate dialogue" while they are engaged in nuclear negotiations with Pyongyang.

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Kim Eui-kyeom made the comments when asked to respond to Mr Trump who said after the summit the US and South Korea should stop their joint military exercises "as long as we are negotiating in good faith".

Mr Kim, Moon's spokesman, says Seoul is still trying to figure out the exact meaning and intent of Mr Trump.

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The round of diplomacy came as there appeared to be confusion over whether US sanctions on North Korea would be lifted.

North Korea's state media has reported that Mr Trump has "expressed his intention" to lift crippling sanctions against the country – despite the US president saying that they will remain until "nukes are no longer a factor".

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But it had always been Mr Kim's goal to rid his country of US sanctions and, according to the state-run KCNA news agency,that is exactly what he achieved.

Following the "meeting of the century", KCNA said Mr Trump had agreed to lift sanctions as relations improve, as well as halt US-South Korea military exercises and offer security guarantees.

There was no US response to the report, but sanctions had not been mentioned in the statement signed by the two leaders at the conclusion of the summit.

U.S. President Donald Trump and North Korea's leader Kim Jong Un shake hands after signing documents during a summit at the Capella Hotel on the resort island of Sentosa, Singapore June 12, 2018
Image: Mr Kim and Mr Trump signed document

At a news conference afterwards, Mr Trump had said he would like sanctions to be lifted but that this would not happen immediately.

Meanwhile, a spokesman for Vladimir Putin said the Russian president welcomed the outcome of the talks with Mr Kim.

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The spokesman said Mr Putin's view was that "there is no alternative to political and diplomatic means in solving the problem of the Korean peninsula.

He added that because of the complexity of the situation, Russia was not expecting a quick resolution, despite the summit.

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