Pompeo, who is trying to arrange a second 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 with which the United States is engaged in escalating trade and diplomatic disputes.
State Department spokeswoman Heather Nauert told reporters Tuesday that the secretary expects to meet with Kim in Pyongyang.
Mr Kim, who as leader has rarely travelled outside of North Korea, met with Mr Trump in June in Singapore in the first summit between the two countries that have never signed a formal treaty to end the 1950-53 Korean War.
North Korea has complained on a weekly basis about the continued United States and global sanctions placed on the country, and on Thursday said the measures were a "source of mistrust".
Speaking before a meeting with South Korean President Moon Jae-in in NY recently, Trump announced that himself and Kim will hold a second summit "in the not too distant future".
The former Ford Motor executive was initially set to join Pompeo on a planned visit to Pyongyang in August.
Nauert said she did not agree that talks had stalled and when asked if Trump's comments on Saturday had been helpful, replied: "I think if our leaders have relatively friendly relations, that that's a good thing".
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"It looks like we'll have a second summit quite soon", he said.
The United States argues the sanctions should remain in place until North Korea has fully and verifiably denuclearized.
On Saturday, Trump lavished praise on Kim and said they had fallen "in love" after exchanging letters.
"The United States is highly unlikely to get on board, especially the Senate, unless there's concrete steps towards denuclearization", she said.
Those incidents, including the Cheonan sinking, were not North Korea attacks but rather "accidental armed conflicts", according to the South Korean military, JoongAng Ilbo reported Thursday.
Even though both sides seemed to be making progress following an announcement that North Korea may be willing to allow global experts to observe the dismantlement of testing sites, Pyongyang and Washington also seemed to entrench their opposing positions during the UNGA. "That that can only help us to achieve our final goal".
Rep. Yoon Young-seok, a spokesman of the main opposition Liberty Korea Party, said in a statement that the two Koreas should reunify under the South's free democratic system and urged North Korea's complete denuclearization.
"We are not easing the pressure in that regard at all", she said, while responding when asked if Washington was considering any kind of peace declaration: "We are not".