Trump said that he would sit down with Kim probably in early June, if not sooner.
Pompeo has taken the lead on the Administration's negotiations with Pyongyang.
His meeting with Kim marks the highest-level meeting between the two countries since 2000, when then-Secretary of State Madeleine Albright met with Kim Jong Il, the current leader's father to discuss strategic issues.
Director of National Intelligence James Clapper visited the country in 2014 to secure the release of two American captives and met with a lower-level intelligence official.
The CIA declined to comment. The White House also declined to comment saying it would not discuss the CIA Director's travels. The North Korean Government also declined to comment.
About a week after Pompeo's trip to North Korea, US officials said that officials there had directly confirmed that Kim was willing to negotiate about potential denuclearisation, according to Administration officials, a sign that both sides had opened a new communications channel ahead of the summit meeting and that the Administration believed North Korea was serious about holding a summit.
"We have had direct talks at very high levels, extremely high levels with North Korea," Trump said today during a bilateral meeting with Japanese Prime Minister Shinzo Abe at Mar-a-Lago, his winter resort.
Trump did not elaborate. The United States has no diplomatic relations with North Korea, but US diplomats have visited and Washington has used several quiet channels to communicate with Pyongyang.
"North Korea is coming along," Trump said. "South Korea is meeting and has plans to meet to see if they can end the war, and they have my blessing on that."
Trump also said he has given "my blessing" to planned discussions between South Korea and North Korea about bringing a formal end to the Korean War, as fast-moving diplomatic developments surrounding nuclear-armed North Korea came into view.
Opening a two-day summit with Abe, Trump took some credit for the rapid developments related to North Korea, whose nuclear and ballistic missile tests his Administration has considered the gravest national security threat to the United States.
Trump said that South Korean officials have "been very generous that without us, and without me in particular, I guess, they wouldn't be discussing anything and the Olympics would have been a failure." Seoul used the Winter Games, held in PyeongChang in February, as a vehicle to reopen diplomatic talks with Pyongyang.
"There's a great chance to solve a world problem," Trump said. "This is not a problem for the United States. This is not a problem for Japan or any other country. This is a problem for the world."