US President Donald Trump has arrived back in Washington after attending the groundbreaking summit with North Korean leader Kim Jong-un in Singapore.
He tweeted that Pyongyang no longer posed a nuclear threat.
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
The president also said North Korea was longer the United States' "biggest and most dangerous problem".
Earlier, North Korea's state media reported that Mr Kim and Mr Trump agreed during the summit to visit each other's countries.
In its first report on the summit, the state-run KCNA news agency said "Kim Jong-un invited Trump to visit Pyongyang at a convenient time and Trump invited Kim Jong-un to visit the US. The two top leaders gladly accepted each other's invitation."
The report said the historic meeting marked a "radical switchover" in the two nations' fraught relations that had "lingered for the longest period on the earth".
The report quoted Mr Kim as saying that ridding the Korean Peninsula of nuclear weapons is dependent on Washington and Pyongyang ceasing moves that antagonise each other.
It added that North Korea and the United States should take legal, institutional steps to guarantee it.
North Korean state media has also said President Trump had agreed during the summit to lift sanctions against the North as well as providing security guarantees.
The KCNA news agency says Mr Trump made the promise after pledging to end joint military exercises with South Korea.
There was no immediate comment about the sanctions claim from the US side.
Mr Trump confirmed the United States will not hold war games with South Korea while North Korea negotiates in good faith on denuclearisation.
"We're not going to be doing the war games as long as we're negotiating in good faith," he told Fox News Channel in an interview in Singapore after the summit.
"So that's good for a number of reasons, in addition to which we save a tremendous amount of money," Mr Trump said.
"You know, those things, they cost. I hate to appear a businessman, but I kept saying, what's it costing?"
US Republican Senator Lindsey Graham said Mr Trump's cost reasoning for halting the exercises was "ridiculous".
"It's not a burden onto the American taxpayer to have a forward deployed force in South Korea," Mr Graham told CNN.
"It brings stability. It's a warning to China that you can't just take over the whole region. So I reject that analysis that it costs too much, but I do accept the proposition, let's stand down (on military exercises) and see if we can find a better way here."
There was some confusion over precisely what military cooperation with South Korea Mr Trump had promised to halt.
The US-South Korean exercise calendar hits a high point every year with the Foal Eagle and Max Thunder drills, both of which wrapped up last month. Another major drill is due in August.
The United States maintains around 28,500 soldiers in South Korea, which remains in a technical state of war with the North after their 1950-53 conflict ended in a truce rather than a peace treaty.
Mr Trump's announcement was a surprise even to President Moon Jae-in's government in Seoul, which worked in recent months to help bring about the Trump-Kim summit.
Asked about Mr Trump's comments regarding the halting of drills, South Korean presidential spokesman Kim Eui-kyeom told reporters there was a need to seek measures that would help improve engagement with North Korea but it was also necessary to confirm exactly what Mr Trump had meant.
President Trump also said yesterday that he would like to lift sanctions against North Korea but it would not happen immediately.
Today, Mr Trump tweeted that his summit with Mr Kim helped bring the world back from "nuclear catastrophe."
The World has taken a big step back from potential Nuclear catastrophe! No more rocket launches, nuclear testing or research! The hostages are back home with their families. Thank you to Chairman Kim, our day together was historic!— Donald J. Trump (@realDonaldTrump) June 13, 2018
At the summit, Mr Trump emphasised what North Korea has to gain by giving up its nuclear weapons and rejoining the international community - a subject he returned to on Twitter.
There is no limit to what NoKo can achieve when it gives up its nuclear weapons and embraces commerce & engagement w/ the world. Chairman Kim has before him the opportunity to be remembered as the leader who ushered in a glorious new era of security & prosperity for his citizens! pic.twitter.com/Xbup4Zyz33— Donald J. Trump (@realDonaldTrump) June 13, 2018
I want to thank Chairman Kim for taking the first bold step toward a bright new future for his people. Our unprecedented meeting – the first between an American President and a leader of North Korea – proves that real change is possible! pic.twitter.com/yF3iwD23YQ— Donald J. Trump (@realDonaldTrump) June 13, 2018