Trump and Kim pledged in a joint statement after their meeting to work towards the "complete denuclearization of the Korean Peninsula," without offering details on how to achieve the goal.
"Major disarmament... We're hopeful that we can achieve that in the two and half years," he said, adding that there is "a lot of work left to do."
When questioned on the wording of the statement, Pompeo said Trump's intention was to allow the US the opportunity to pursue further productive conversations on the issue with Pyongyang.
"Let me assure you that 'complete' encompasses verifiable in the minds of everyone concerned. One can't completely denuclearize without validating, authenticating," he added.
Pompeo also said he anticipates the US would next speak to DPRK officials "fairly quickly after we return to our home countries," adding that he was "very confident" that some form of engagement between the two sides would take place in the next week.
On Military drills
Trump unexpectedly announced that the US would halt joint military exercises with its security ally Seoul at his post-summit press conference.
Pompeo defended Trump's stance from Seoul, saying the joint drills could be brought back if negotiations with the DPRK deteriorated.
"He (Trump) made it very clear that the condition precedent for the exercises not to proceed was a productive, good faith negotiations being ongoing," Pompeo told reporters.
The US stations 28,500 troops in the ROK to help protect it from its northern neighbor.
Pompeo was in the ROK to brief officials on the outcomes of the summit between Trump and Kim.
This is the first official visit by the top US diplomat to the ROK since he took office in April.
On Thursday, Pompeo will meet with the country's Foreign Minister Kang Kyung-wha and Japan's top envoy Taro Kono.
The Blue House said Wednesday it needs to consider ways to make the dialogue between the DPRK and the United States go on smoothly after US President Donald Trump commented on the halt of the ROK-US military exercises.
Japan's Defence Minister Itsunori Onodera pointedly on Wednesday also said the drills played a "vital role in East Asia's security," expressing concern about their cancellation.
"I hope to share this recognition between Japan and the US, or among Japan, US and South Korea," he told reporters.