When asked whether North Korean officials would meet with USA officials during their visit, he said the delegations were at different levels.
While China and Russian Federation have said the United Nations should consider relaxing sanctions on North Korea, Trump insisted on Sunday that they would remain "in full force and effect" until the USA sees "very positive" results in the nuclear issue.
Rumors of another visit came late Monday night as a North Korean train passed into the Chinese city of Dandong under heavy security.
The South Korean newspaper JoongAng Ilbo previously reported that Mark Lambert, a senior U.S. State Department official handling North Korea issues, visited Vietnam in December.
Unlike that occasion, when the North's state media waited until his return to announce his journey, the official KCNA news agency said on Tuesday that he was traveling on board his "private train".
Kim's visit comes as a USA delegation opened a second day of talks with Chinese counterparts in Beijing aimed at ending the trade war between the world's two largest economies.
China is a key diplomatic ally of North Korea and one of the country's main sources of trade and aid.
"The Chinese have been very clear to us that these are separate issues", Pompeo said in an interview with CNBC on Monday.
While there have been tensions between Beijing and Pyongyang, the two Korean War allies retain close ties, with China being North Korea's most important ally as the two nations face off against the United States.
Since the Singapore summit, there is growing scepticism in the USA over Kim delivering on his promise to do away with the nuclear programme despite Washington's assurance over North Korea's security.
Chinese Vice-Premier Liu He made a surprise appearance on Monday to greet the USA delegation of mid-level officials, a sign of China's willingness to avert a full-blown trade war.
The disappearance of Jo Song Gil, North Korea's acting ambassador to Italy, could create a publicity headache for North Korean leader Kim Jong Un as he pursues diplomacy with Washington and Seoul and seeks to portray himself as an global statesman.
The last senior North Korean diplomat known to have defected is Thae Yong Ho, a former minister at the North Korean Embassy in London, who fled to South Korea in 2016.
"Their behavior has demonstrated that as well and we appreciate that".
He also visited China three times, notably without a reciprocal visit from Mr Xi in a break with diplomatic convention.
Possibly fearing the economic effect of crushing outside sanctions imposed because of his weapons' tests, Mr Kim abruptly turned to diplomacy with Seoul and Washington previous year.
Denuclearization talks have sputtered since Trump and Kim held an unprecedented June meeting in Singapore, with Washington and Pyongyang each calling on the other to take action. Some reports say he's under the protection of the Italian government and wants to seek asylum in the U.S. The Italian government said last week, though, that Jo has not asked for asylum.