The United States and North Korea are technically still at war - a stop-gap armistice ended the brutal three-year Korean war in 1953 and around 30,000 American troops remain in neighboring South Korea, which the USA supported in the conflict.
He says he had "good" and "substantive" conversations with leader Kim Jong Un during his visit.
Abe said he is open to holding talks with Kim only when that would lead to a settlement of the abduction issue.
Many observers have warned Kim's regime will try to drive a wedge between the allies as the summit approaches, playing Seoul's fear of war against Washington's nuclear concerns.
She said that the idea of the USA reducing its military footprint in South Korea wasn't on the table.
The Trump-Kim summit is scheduled to take place on June 12 in Singapore.
Watch Pompeo's opening statements at the press briefing below..
Kim's regime also carried out missile tests that convinced U.S. intelligence officials, including Pompeo in his former role as CIA chief, that North Korea could threaten USA cities.
But despite the optimism of that moment, all efforts to limit North Korea's nuclear program have, to date, failed. "Our conversations were warm, we were each representing our two countries" and working to share an understanding of their objectives were, Pompeo said.
But he stressed that this would require a "robust verification" programme by the USA and other nations. "We talked about the truth that America has usually in historical past had adversaries that we are actually shut companions with".
During their summit at a border truce village, Moon and Kim vaguely promised to work toward the "complete denuclearization" of the Korean Peninsula, but made no references to verification or timetables.
"There's a danger here of the peace track moving more quickly than the denuclearization track", warned Abraham Denmark, an Asia expert and former senior U.S. defense official.
The top USA diplomat said the release of three American detainees set the conditions for a successful summit between the US and North Korea. Kim Dong Chul had been in custody since late 2015.
When asked to define what he meant by permanent, verifiable denuclearization, Pompeo said, "I'm not sure how to define it fully, it's pretty clear what that means. how to ensure North Korea doesn't possess the capacity to threaten the world".
But Pompeo said he believes he's reached an understanding with Kim about what's on the table for negotiation.
After her talks with Pompeo, she took pains to "emphasize again that the US military presence in Korea is a matter for the ROK-US alliance first and foremost".