The revival of the summit came after Trump met with a North Korean emissary on Friday afternoon at a meeting that extended for almost two hours, much longer than was expected.
Trump was meeting in the Oval Office with Kim's envoy, Kim Yong Chol, a former spy chief and now the country's top nuclear negotiator.
The man Trump met on Friday, Kim Yong Chol, had come to Washington after a day of talks with Pompeo to see whether a summit might be possible.
After the meeting, Trump and Kim Yong Chol posed for photos on the White House lawn. Kim is likely to receive a proposal that he would have to refuse on June 12, which would prompt a reaction from Washington, Glazebrook added. Trump called it a "very nice letter".
Pompeo said he believes North Korea is contemplating a new strategic path forward, but he cautioned that the country would "have to choose a path that is fundamentally different" to achieve security - meaning complete, verifiable, irreversible denuclearization.
Trump pledged to keep sanctions on North Korea until it ends its nuclear program. "He'd like to see it happen", the president said.
Cho Myoung Gyon, the South Korean unification minister, warned this week that "significant" differences remain between the US and North Korea on how to achieve denuclearization.
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A top North Korean official has departed the White House after meeting with President Donald Trump amid negotiations over a high-stakes summit.
But then, just minutes later, Trump admitted he hasn't even opened the letter, let alone read it.
Kim Yong Chol was greeted Friday by White House chief of staff John Kelly, who brought him inside the White House to meet President Donald Trump.
Kim's right hand man General Kim Yong Chol flew into NY on Wednesday to discuss preparations for the assembly.
Trump also said that the USA would not impose any additional sanctions on North Korea for the time being.
Kim Yong Chol, vice chairman of North Korea's ruling party executive and a veteran regime insider, arrived for his Oval Office encounter accompanied by the senior U.S. officials who have overseen an extraordinary diplomatic opening.
North Korea, whose nuclear ambitions have been a source of tension for decades, has made advances in missile technology in recent years but Trump has sworn not to allow it to develop nuclear missiles that could hit the United States. "As we move to adjust to the political situation in the face of USA hegemonism, I am willing to exchange detailed and in-depth opinions with your leadership and hope to do so moving forward", Kim told Sergey Lavrov. Kim needed a special waiver from the State Department to travel to NY and to Washington. A letter being delivered to me from Kim Jong-un.