Mr Pompeo will also press for the release of three US prisoners from the country.
He said that he hopes North Korea will "do the right thing".
The time and date of Mr Trump's planned meeting with Mr Kim has now been agreed on, but he has yet to reveal where or when it will happen.
Former CIA chief Mr Pompeo met Kim Yong Chol, vice chairman of the central committee of North Korea's ruling party, for lunch.
The pair discussed the possible agenda for the meeting.
"For decades, we have been adversaries. Now we are hopeful that we can work together to resolve this conflict," Mr Pompeo said.
"For decades, we have been adversaries. Now we are hopeful that we can work together to resolve this conflict," Mr Pompeo said.
It is his second visit to North Korea - he visited at Easter before he was officially appointed as America's top diplomat.
"We think relationships are building with North Korea. We will see how it all works out. Maybe it won't. But it can be a great thing for North Korea, South Korea and the entire world," Mr Trump said.
Asked whether the three Americans held in North Korea would be freed, Mr Trump told reporters: "We'll all soon be finding out. We'll soon be finding out. It would be a great thing if they are."
Mr Trump broke the news while announcing his plans to withdraw from the Iran nuclear agreement.
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