On Thursday, the North Korean leader said he had received a letter from Trump, and was impressed by Trump's "unusual determination and will" to come to an agreement.
Kim's upbeat, if cautious, tone Thursday suggested that both sides have recently narrowed their differences enough to discuss the details of a second summit. However, Pompeo has given varying statements about the degree of the White House's patience.
The delegation, led by Ri Su-yong, vice chairman of the ruling party's Central Committee, arrived at a Beijing train station at around 11 a.m. and was greeted by North Korean Ambassador to Beijing Ji Jae-ryong and Chinese officials.
A number of letters have been exchanged between the pair since their historic meeting in Singapore last June.
The White House publicly maintains its position to continue pressuring Pyongyang with sanctions until the regime takes affirmative steps toward denuclearization, but gradually these buttons may be unclasped to reward North Korea's "good" behavior.
The report added that Kim had "set forth tasks and orientation for making good technical preparations for the second DPRK-U.S. summit". However, satellite images show that North Korea is continuing to develop ballistic missiles at several hidden bases, NPR has reported.
Earlier this week, Secretary of State Michael Pompeo told the World Economic Forum in Davos the private sector is poised to step in and boost North Korea's staggering economy if it gives up its nuclear ambitions.
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He called the Trump-Kim dialogue "promising" but stressed that "we still await concrete steps by North Korea to dismantle the nuclear weapons that threaten our people and our allies in the region".
Pompeo, who made several trips to Pyongyang a year ago, sought to meet his counterpart last November, but the talks were called off at the last minute.
North Korea has hinted, for example, at the possibility of agreeing to the USA demand for verification of denuclearization efforts before it discards its Yongbyon nuclear facilities.
The two sides have given no sign of having narrowed their differences over USA demands that North Korea abandon its nuclear weapons program and Pyongyang's demands for a lifting of economic sanctions and a formal end to the Korean War.
Pyongyang needed to take "bold, practical measures for denuclearisation" to ensure sanctions are lifted, he told reporters, but added that "corresponding measures" were also needed from the USA, such as agreeing a "peace regime" and formally declaring an end to the 1950-53 Korean War.
Mr Pompeo said on Tuesday that there remained "an very bad lot of work to do" to achieve denuclearisation but he anticipated more progress by the end of February.
Kim's latest trip to China, his fourth since previous year, came as the North's strongest ally has encouraged negotiations with the US while at the same time arguing in favor of immediate easing of sanctions.
2015 after China reportedly took issue with aspects of the performance featuring the North's nuclear and missile development.