President Donald Trump and Kim agreed to denuclearization only in vague terms at their summit in Singapore, the first meeting between leaders of the USA and North Korea.
The State Department talking head, Heather Nauert announced that Pompeo and Kim will meet in Pyongyang on October 7.
"It looks like we'll have a second summit quite soon", he said.
For now, Pompeo may explore how serious North Korea is in its offer to dismantle Yongbyon, and what it wants in return; and then to decide if that represents a sound basis for another meeting between Trump and Kim, something both leaders appear keen to make happen.
"We want it fast, but we're not going to play the time game", he said, adding that his reference last month to 2021 was repeating a comment made by the North and South Korean leaders at a summit last month in Pyongyang.
He will also travel to Japan, South Korea and China on his swing through Asia, she said.
On Saturday, Trump lavished praise on Kim - considered by human rights groups to be one of the world's most repressive leaders - and said they had fallen "in love" after the exchange of letters.More news: Amy Schumer, Emily Ratajkowski among more than 300 arrested at Kavanaugh protest
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Critics have pointed out that the Singapore declaration contained no firm commitments from North Korea to dismantle its nuclear and missile programs and United States officials have expressed frustration at North Korea's evasion of sanctions.
He said in a statement last month the United States aimed for North Korean denuclearisation by that date, but a week later Trump said he did not have a time frame. Washington has also resisted calls to relax tough worldwide sanctions.
Pompeo will open his trip on Saturday in Tokyo, where he will meet Prime Minister Shinzo Abe, who has long championed a hard line on North Korea but recently said he was willing to meet Kim.
Experts differ about North Korea's sincerity: some like Narang say it has no real interest in disarmament and is instead just milking the process for whatever benefits it can get.
"The DPRK is taking substantial and crucial steps to implement the joint statement made at the DPRK-US summit, but the US is still trying to subdue someone by resorting to sanctions", the commentary accused. "That that can only help us to achieve our final goal".
"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". "Our policy has not changed".
Pompeo's trip to China comes at a time of deteriorating relations and tit-for-tat tariffs sparked by Trump's accusations of unfair Chinese trade practices.
Pompeo is expected to lay the groundwork for a second U.S.