President Trump and Kim will fly into Singapore for a meeting on June 12 to discuss the potential for denationalization and greater cooperation between North and South Korea.
After the meeting, which lasted more than an hour, Trump walked Kim out of the White House and they continued to speak and posed for a photo before Kim got into a black SUV and departed.
The president told reporters "we're going to deal".
The president said he believed Kim wanted a deal.
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Peña Nieto quickly replied on Twitter , in English and in Spanish, saying Mexico will never pay for the wall, "Not now, not ever". I don't want to cause it. "I don't want to cause a problem, but in the end, Mexico's going to pay for the wall".
"I don't even want to use the term "maximum pressure" anymore", Mr Trump added, referencing his preferred term for the punishing United States economic sanctions against North Korea.
"I look forward to seeing what's in the letter", Trump said on Thursday as he left Joint Base Andrews for a trip to Houston.
Plans for the high-stakes sit-down in Singapore had been cast into doubt.
But continuing differences led Trump to abruptly cancel the planned summit last week, and then quickly announce it might still be held as scheduled. He said the June 12th summit may just be the beginning of talks, and that working towards denuclearization may take more than one conversation or meeting. Trump had mused that Kim's "attitude" had changed after the North Korean leader's surprise visit to China two weeks ago, suggesting China was pushing Kim away from the table.
On the same day in Pyongyang, Kim Jong Un told Russia's Foreign Minister Sergei Lavrov that his commitment to denuclearisation remains "unchanged and consistent and fixed", but experts warn that he will likely seek deep concessions from Washington. By the next day, he was signalling the event could be back on after a conciliatory response from North Korea.
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Mr. Trump said he thinks Kim Jong Un is committed to denuclearization.
1 June: Senior North Korean envoy Gen Kim Yong-chol delivers a letter from Mr Kim in person at the White House.
Previous attempts to negotiate with North Korea have failed, but earlier this year Pyongyang held direct talks with Seoul and the two Korean leaders held a historic summit in April.
Wall Street took word from Trump that the summit was back on in stride. Pompeo and Chief of Staff John Kelly were also spotted inside the Oval Office for the meeting with President Trump.
Pompeo spoke after meeting with Kim Yong-chol for a little more than two hours at the residence of the deputy US ambassador to the United Nations.
U.S. Secretary of State Mike Pompeo and a senior North Korean official met in New York Wednesday as both sides push to salvage a highly anticipated summit between their leaders.
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Harris has been nominated to become the next US ambassador to South Korea. Philip Davidson, the new head of U.S. Pacific Command, said in April.
"I'm still convinced that if he's in this process, even if the summit is ongoing and we're moving out, if this thing isn't heading towards the obvious objective he'll pull out".