The opposition has long taken a more sceptical view of Kim’s intentions.
Pompeo departed from Tokyo, where he spent the first leg of a tour that will include stops in Pyongyang, South Korea and China.
China and Russia have said the UN Security Council should reward Pyongyang for steps taken after US President Donald Trump and North Korean leader Kim Jong Un met in June.
South Korean President Moon Jae-in faces his toughest challenge yet: delivering something substantive that goes beyond previous vague statements on denuclearization.
Bolton said US Secretary of State Mike Pompeo is prepared to return to North Korea for another meeting with Kim.
Trump suggested that China, North Korea's chief ally, might be interfering in reaction to the Trump administration's stance on US-China trade.
While President Donald Trump’s point man for nuclear talks summed up his 27 hours in the North Korean capital as “productive,” the regime called the visit “regretful.”
The State Department on Thursday denied that the United States had softened its approach toward North Korean denuclearization, as US Secretary of State Mike Pompeo heads to Pyongyang hoping to hammer out a roadmap for its nuclear disarmament.
The State Department said Pompeo would head on Saturday from Pyongyang to Tokyo, where he would discuss North Korean denuclearization with Japanese and South Korean leaders.
Putin and Moon agreed to joint research in the fields of electricity, gas and railways in order to advance cooperative projects between North Korea, Russia and South Korea.
The North Korean leader also promised during a meeting with Xi in Beijing to cooperate with Chinese officials to secure "true peace" in the process of "opening a new future" on the Korean peninsula.
New US Secretary of State Mike Pompeo said he had a "good conversation" with North Korea's Kim Jong Un during his visit to Pyongyang, adding Kim was "prepared to... lay out a map that would help us achieve" denuclearization.
Kim had delivered a report "on the development of the recent situation on the Korean peninsula", including the separate summit with South Korea to be held later this month.
It is the first time the offer was made directly to Washington, after it was previously conveyed through South Korean national security adviser Chung Eui-yong.
President Donald Trump is ready to meet North Korean leader Kim Jung by May in response to Kim's invitation to hold the first-ever U.S.-North Korea summit, a South Korean envoy said, marking a potentially dramatic breakthrough in the North Korea nuclear standoff.
Trump credited "very, very strong" sanctions and the "big help" of China for North Korea's offer to enter into talks.