Pompeo said that after a series of meetings he believes the talks are going in "the right direction".
Though he's accused of the Sony pictures 2014 hack and was sanctioned by the US, Kim Yong Chol was feted at the White House.
Trump pledged to keep sanctions on North Korea until it ends its nuclear program.
"I look forward to the day when I can take the sanctions off of North Korea", Trump said. Agreeing to reopen the summit, based on a meeting about a letter that Trump hasn't read, makes no sense.
"That letter was a very nice letter".
Plans for the high-stakes sit-down in Singapore had been cast into doubt.
Trump's made-for-television announcement on Friday was the latest twist in the trans-Pacific political and diplomatic drama that at times unfolded in real time, and has been closely-followed on social media.
The White House emphasized that it has remained in close contact with South Korean and Japanese officials as preparations for the talks continue. Instead, the officials said, it brought both sides to the table with increasing seriousness, as they work through myriad logistical and policy decisions to keep June 12 a viable option for the summit.
President Trump's remarks follow months of pressure from China and South Korea on Washington to invest in the economic reconstruction of North Korea, ravaged by almost a century of oppressive communist rule. North Korea's conciliatory response to that letter appears to have put the summit back on track.
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After arriving at the White House on Friday afternoon, the North Korean official was seen being ushered into the West Wing by the president's chief of staff, John Kelly. Kim Yong Chol is the highest-ranking North Korean official to visit the United States in almost 20 years.
Meanwhile, North Korea suggested during high-level talks on Friday that the two Koreas hold a joint celebration of the anniversary of a historic 2000 inter-Korean summit this month in the South, an official in Seoul said.
Most expert observers are sceptical that even an unprecedented summit between the two leaders can lead to a rapid breakthrough, and Trump admitted it would be a long and hard process.
The meeting was the first ever between the North Korean leader and a Russian official - and Lavrov used the opportunity to invite Kim for a return fixture in Moscow.
"Good working dinner with Kim Yong Chol in NY tonight", Pompeo tweeted Wednesday.
Secretary of State Mike Pompeo, the former Central Intelligence Agency chief who has travelled to North Korea and met with Kim Jong Un twice in the past two months, said he believed the country's leaders are "contemplating a path forward where they can make a strategic shift, one that their country has not been prepared to make before".
Kim says he is committed to "denuclearisation" in some form, but he is expected to demand security guarantees - one of which could be an formal end to the conflict with the US and South Korea.
"We will push forward to test the proposition that we can achieve that outcome", he said.
On Wednesday, Russian Foreign Minister, Sergey Lavrov met the North Korean leader, Kim Jong-un in one of his rare visits to Pyongyang, North Korea.
Though the United States is engaged in three separate sets of talks with North Koreans around the globe, it's still unclear whether Trump will actually meet with Kim.