Pompeo, who is trying to arrange a new summit between Kim and US President Donald Trump, will also head to US allies Japan and South Korea, as well as North Korea’s chief ally China, spokeswoman Heather Nauert said.
Pyongyang is hopeful of securing relief from punitive economic sanctions in any deal.
“I think it shows momentum that he is paying his fourth trip,” Nauert told reporters.
“Everybody recognizes that there is a ways to go,” she said, but added: “We feel confident enough to hop on a plane to continue these negotiations.”
The invitation to return to Pyongyang to discuss North Korean denuclearisation efforts was made during a meeting with North Korean Foreign Minister Ri Yong-ho on the sidelines of the United Nations General Assembly last week.
After the trip to Pyongyang, Pompeo will head to Seoul, where he will meet President Moon Jae-in, who has helped spearhead the reconciliation efforts with North Korea.
Nauert said Pompeo would head afterwards to Beijing for meetings with unspecified officials.
Kim and Trump met in June in Singapore in the first-ever summit between the two countries that have never signed a peace treaty to formally end their 1950-53 war.
On Saturday, Trump lavished praise on Kim and said they had fallen “in love” after exchanging letters.
Human rights groups consider Kim to be one of the world’s most repressive leaders.
Trump paints rapprochement with North Korea as a signature foreign policy achievement, although critics question whether Pyongyang has taken any firm action.
The US has insisted on maintaining tight UN sanctions against North Korea during the diplomatic drive, while Beijing has said it is time to start easing sanctions.
Kim has committed to giving up his country’s nuclear weapons although his actions have fallen short of Washington’s demands for a complete inventory of North Korea’s weapons programmes and irreversible steps to give up a nuclear arsenal that potentially threatens the US.