© KCNA / ReutersNorth Korea's Hwasong-15 rocket test is pictured on November 29, 2017.
Pompeo said he will be playing the lead role when it comes to ensuring progress with Pyongyang, and added that he is confident the US would begin its next engagement with North Korea "in the next week or so."
According to the secretary of state, there were "lots of other places" on which Trump and Kim reached understandings, but were not included in the final Singapore document. Those topics will be revisited when talks resume.
Despite the meeting being hailed a success by Washington, Pompeo stressed that there is still "a great deal of work to do... a long way to go with North Korea."
The landmark meeting between the two leaders on Tuesday ended in Trump and Kim signing a joint statement in a move which is being seen as a friendly way to keep talks going, with Washington ultimately seeking denuclearization of the Korean peninsula.
Trump also vowed to end joint military exercises with South Korea, as Pyongyang has long viewed such exercises as a provocation and preparation for war. The concession by Trump is in exchange for North Korea freezing its weapons tests.
While Pompeo says there is still a lot of work to be done, Trump felt immediately confident about his meeting with Kim, tweeting less than a day after the event that there is "no longer a nuclear threat from North Korea." He said that, before he took office, Americans thought the US was going to war with North Korea, and noted that his predecessor Barack Obama had called Pyongyang "our biggest and most dangerous problem."
Comment: Such a goal could be admirable if it weren't for the United States' history of destroying countries after disarming them.