The annual Ulchi Freedom Guardian joint exercise is scheduled for August.
Following the consultations with his South Korean and Japanese counterparts, Pompeo was heading to China on a similar mission later on Thursday.
"We're going to get complete denuclearisation and only then are we going to lift sanctions", Mr Pompeo added.
Japanese media, including Jiji Press, said Japanese foreign ministry officials "contacted" their North Korean counterparts Thursday at an worldwide security conference in Mongolia.
But details on what form those promises would take were sparse, with critics noting the lack of a timeline for when North Korea will begin dismantling its nuclear programme.
Hailing his meeting with Kim, the first between a sitting United States president and a North Korean leader, as a major win for American security, Trump indicated that he expects Pyongyang to follow through on its commitment to work toward denuclearization, Reuters reports.
He said there were good reasons for North Korea to come to the negotiation table and start the denuclearisation process.
Pompeo was also urging skepticism after North Korean official media said Trump had agreed to a step-by-step approach to denuclearization.
Many lawmakers from both parties, while unready to declare the summit a diplomatic victory or defeat, remained skeptical the USA could successfully negotiate a deal toward peace with Kim - but are letting the process play out. Because complete encompasses verifiable and irreversible.
"Everybody can now feel much safer than the day I took office", he wrote on Twitter.
Russian Federation has encouraged de-escalation talks between the USA and North Korea.
Now, when questioned about the human rights abuses in North Korea, the President has defended "tough guy" Kim. Despite some concerns among allies and analysts, the Trump administration continues to tout the summit as a success, and Pompeo said earlier that he hopes to see "major disarmament" of North Korea by 2020.
The Sankei Shimbun said Kim discussed the possibility during historic talks Tuesday with US President Donald Trump.
Late previous year, for example, she announced North Korea's test of what it said was a hydrogen bomb, telling viewers it was a "perfect success". Gen. Kim Do-gyun told reporters before the talks. Kim's commitments did not appear to go beyond what he already pledged to do in April when he met with South Korean President Moon Jae-in along their countries' border.
"The issue of South Korea-U.S. joint exercises is one that should be discussed", Kang said. "But the issues of the alliance should be dealt with under the premise we maintain joint ironclad defence posture".