But, briefing reporters before flying on to Tokyo, he offered few new details as to how North Korea would honour its commitment to "denuclearise" in exchange for U.S. security guarantees.
Pompeo has the crucial task of dispelling growing scepticism over how seriously Kim is about giving up his nuclear arsenal and translate the upbeat rhetoric following the first meeting between leaders of the U.S. and North Korea into concrete action.
The North's relatively harsh tone contrasts somewhat with what Pompeo said after holding talks with Kim Yong-chol, a close aide to North Korean leader Kim Jong-un, for two straight days from Friday, though he also admitted that there was "more work to be done".
Kim did not comment on the issue of denuclearization, saying only that there "are things I have to clarify".
The talks between Pompeo and Kim Yong Chol were the first high-level, face-to-face meetings since Trump and Kim met in Singapore on June 12 and reached an agreement to work toward denuclearization of the Korean peninsula, among other things. "There's no - no one walked away from that, they're still equally committed, Chairman Kim is still committed".
Mr Pompeo said more talks are needed on both.
Secretary of State Mike Pompeo is pictured returning to a meeting with North Korea's Kim Yong Chol (not pictured).
Poachers eaten by lions on South Africa game reserve
According to The Daily News the lawmen found a head, limbs, other body parts along with three pairs of empty shoes by a lion camp. Police forensics teams' investigations are ongoing, and the number of poachers killed can not be confirmed, said the statement.
Pompeo's talks will be closely watched in the region.
Pompeo also said that a team would be meeting with officials around July 12 to discuss the repatriation of remains of US soldiers, and that talks would be held about the destruction of North Korea's missile engine testing facility. But ever since the announcement of that summit, experts on North Korea have warned that Kim was very unlikely to give up his nuclear arsenal altogether, since it is his prime source of leverage against the rest of the world.
She said USA national security adviser John Bolton and White House chief of staff John Kelly were also on Pompeo's earlier briefing call with Trump.
As they began their talks on Saturday, Kim Yong Chol alluded to the fact that Pompeo and his delegation had stayed overnight in Pyongyang.
Pompeo, who spoke with Trump, national security adviser John Bolton and White House chief of staff John Kelly by secure phone before starting Saturday's session, replied that he "slept just fine". "Our policy toward North Korea has not changed, we're committed to a denuclearized North Korea".
"We had anticipated the USA side would come with a constructive idea, thinking we would take something in return", the North Korean spokesperson said. Trump said after the Singapore summit that Kim had agreed to send the remains back to the United States.
Pompeo had said before the Singapore summit Trump would reject anything short of "complete, verifiable and irreversible denuclearisation".
The spokesman said that the first high-level talks between the two countries following the summit have failed to consolidate mutual trust, only to risk undermining the North's commitment to denuclearization.