The report by the official Korean Central News Agency did not say when the visit would take place, but the two sanctions-hit nations have been allies for decades and Washington has accused the North of assisting Syria with its weapons programmes.
"We're going to deal", Trump told reporters moments after the meeting ended.
In response to Trump's letter, the DPRK's First Vice Foreign Minister Kim Kye Gwan said Friday that the country is ready to sit down with the United States any time in any manner for talks to solve the problems existing between them.
In the latest sign of hostility cooling down but hopes kept in check, Trump said he's unilaterally put a hold on new sanctions against the North "until the talks break down".
KELLY: And, Scott, do we have any more insight into what would count as a successful summit from the North Koreans' point of view, what they want in exchange for at least starting talks about maybe giving up their nukes?
"Obviously if the diplomats can do their work, if we can reduce the threat, if we can restore confidence-building measures with something verifiable, then of course these kinds of issues can come up subsequently between two sovereign states (South Korea and the US)", said the Pentagon chief.
"It seems as if the road to a North Korea-U.S. summit has become enhanced and expanded", Kim Eui-kyeom, a Seoul government spokesperson, said in a statement hours after Trump had made his announcement.
Kim Yong Chol delivered a personal letter to Trump from the North Korean leader. "We call on all involved sides to fully appreciate their responsibility for not allowing this very important but still fragile process to break down", he said, adding that Russian Federation was ready to contribute to ongoing diplomatic efforts.More news: Tiger Woods Struggles Late, Finishes 2018 Memorial Tournament at 9 Under
"We'll be meeting on June 12 in Singapore".
Kim is expected to president a letter from Kim Jong Un (kim jawng oon), the North Korean dictator, to Trump. At the time he pulled out, they said the North Koreans had been ignoring USA entreaties, hadn't been answering the phone.
South Korean President Moon Jae-in, who has met Kim twice in recent weeks, has lobbied hard for a meeting between Trump and Kim.
Pompeo warned at a news conference after talks with Kim Yong Chol in NY on Wednesday and Thursday that the path to better relations would not be easy.
Separate talks have been going on in Singapore and along the Demilitarized Zone along the border between North and South Korea.
Kim Yong Chol delivered a letter from the North Korean leader to Trump.
Trump has refused to publicly acknowledge whether he's spoken directly with Kim Jong Un ahead of the talks.
The United States and South Korea blacklisted the official for supporting North Korea's nuclear and missile programs in 2010 and 2016, respectively.
But he said that, after what have now been two meetings with Kim Jong Un and three with Kim Yong Chol, he believes the North is at least ready to consider addressing USA demands for denuclearisation.