Donald Trump believes Kim Jong Un will not break his promise to the denuclearisation deal.
Pompeo is confident that North Korean leader Kim Jong Un would live up to his commitment not to resume nuclear and missile testing.
An official also confirmed Washington would seek Pyongyang's 'clarification on the purposes' of rebuilding a long-range rocket launch site.
North Korea's foreign minister said the country only wanted some of the measures eased, and the offer to "all the nuclear production facilities" in Yongbyon was the best deal it could offer.
Pyongyang holds US responsible for the UN sanctions imposed on it over its banned weapons programmes.
Vague statements from Donald Trump spark doubts about the progress made with Kim Jong-un, as the summit in Hanoi concludes without a public signing ceremony.
The 1st historic summit in Singapore produced little more than a vaguely worded document committing to 'complete denuclearisation'.
The 2 men who once traded personal insults and threats of destruction are holding their 2nd meeting in 8 months.
The two sides might be able to agree to a formal end of the Korean War, which the North has long called for as a major step towards normalising ties.
Pyongyang sees denuclearisation more broadly, seeking an end to sanctions and what it sees as US threats.
Speculation is building that the US and North Korea could agree to a treaty in return for denuclearisation measures and the withdrawal of US troops might follow.
The train's crossing into China follows days of speculation over Kim's secretive travel plans to Hanoi.
President Moon Jae-in says that he is ready to undertake anything from reconnecting rail and road links between the two Koreas to other inter-Korean economic cooperation.
Stephen Biegun, the US Special Representative for North Korea, said preparatory talks had been productive.
What the two leaders hope to achieve remains a mystery.
Kim Yong-chol's trip comes as expectations grow for a second US-North Korean summit after Kim Jong-un last week went to Beijing.
North Korea is demanding relief from the multiple sanctions over its banned nuclear weapons and ballistic missile programs.
Kim Jong Un expresses an intention to meet with Moon frequently in 2019" to pursue peace and solve the issue of denuclearising the peninsula together.
North Korea rejects American calls for it to unilaterally denuclearise.
Biegun is scheduled to hold talks on Thursday with his South Korean counterpart, Lee Do-hoon.
The warning from the Pyongyang came days after the US said it was imposing sanctions on three senior North Korean officials over human rights abuses.
The North's stinging response came after the United States said it had introduced sanctions on three North Korean officials.
Kim's first observation of a weapons test this year could complicate already stalled nuclear talks with the United States.
It marked the first official report of a weapons test by North Korea since it began a delicate diplomatic process with Washington over its nuclear and missile programme.