"We did have very serious discussion on very important matters yesterday", Mr Kim said.
Amid increasing scrutiny of North Korea's commitment to giving up its weapons, Pompeo came to Pyongyang in a bid to hammer out the details of a denuclearization plan.
But Kim has yet to provide details of how or when North Korea might dismantle a weapons program that Trump has vowed will not be allowed to threaten the United States.
'People are going to make stray comments after meetings, ' Pompeo said.
But despite the very negtive views about the meeting, . the statement was careful about criticizing President Trump, and said that they still cherish their good faith in him.
"So, thinking about those discussions you might have not slept well."
Before Pompeo's meeting with Kim Yong Chol there were hints of disagreements between the two sides. Department of Defense officials will meet with North Korean counterparts on July 12 to discuss the return of the remains. "We pushed them really hard to live up to the commitments of the president, and they may be reacting to save face", a source, who asked not to be named, told ABC News.More news: Russian Federation loses to Croatia, and Twitter users Putin their best jokes
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All along, however, experts had wondered how the USA and North Korea would bridge differences that have bedeviled their talks for decades and only seemed exacerbated under Trump.
Our correspondent at South Korea's foreign ministry, Lee Ji-won, is on the line for us.
The alleged gift came after the song became a point of discussion for Trump and Kim during their summit in Singapore last month. The last time the two leaders exchanged letters was in early June when Kim Yong Chol - the country's former spy chief and now the vice chairman of the Workers' Party Central Committee - brought a letter to the White House for Mr. Trump on behalf of the leader.
It would be worse for Trump himself.
'Dealing with North Korea is hard because Kim Jong Un wants it to be hard, ' said Russel, who was assistant secretary of state for East Asian and Pacific Affairs in the Obama administration.
North Korean state-run news agency KCNA on Saturday claimed the USA was using a "gangster-like mindset" in pushing for the country to abandon its nuclear program. On his way home from Singapore, Trump declared that North Korea no longer posed a nuclear threat to the US.
In recent days, intelligence reports have shown that North Korea is continuing work at a key rocket-engine facility.
The US-North Korea talks are being closely watched across Asia.
"Nothing could be further from the truth", State Department spokesperson Heather Nauert said in response.
The U.S.is "fatally mistaken" if it thinks North Korea can be pressured into accepting its demands, the statement continued, adding that a breakdown in the North Korean-U.S. relationship would mean "there is no guarantee that this will not result in yet another tragedy".
Pompeo has bristled at the idea that the Singapore declaration was an empty promise, saying repeatedly that Kim Jong Un had assured him in private conversations he was ready to give up his nuclear arms.