Pompeo's remarks contrasted sharply with comments from a senior defense official who briefed reporters ahead of a trip to Asia by U.S. Secretary of Defense Jim Mattis and said Washington would soon present a timeline to North Korea with "specific asks".
The 1950-53 Korean War, and the devastation the country suffered at the hands of the United States and its allies, remain a major part of every North Korean's education.
State media referred to Trump quite deferentially in their reports of the summit, calling him by his full name and adding the title of president of the United States of America - itself a somewhat jarring contrast to the way it normally spits out merely the surname of USA officials, with no titles.
Senior administration officials said that Pompeo was seeking an early meeting with his North Korean counterpart to begin discussions about next steps.
Officials agreed to permit a reunion of 100 separated family members to meet on August 20 to 26 at the Mount Kumgang area in North Korea.
Turkey election: Polls close as Erdogan seeks second term
Opposition parties and NGOs deployed up to half a million monitors at ballot boxes to ward against possible electoral fraud. AK Party supporters clogged a main road in the capital Ankara leading to party headquarters honking horns in celebration.
Abe, grappling with domestic scandals, has vowed not to rest until the others return as well, an issue he pressed U.S. President Donald Trump to raise at his June 12 summit in Singapore with Kim.
US Secretary of State Mike Pompeo may bring back the remains when he visits North Korea, according to Korean news reports.
Trump announced last week that North Korea returned the remains of 200 USA or allied service members lost in the Korean War, while the Pentagon announced on Friday it would indefinitely suspend two training exercises with South Korea.
"If we can't do that, if it turns out that there is no capacity to deliver the outcome that both presidents said they wanted, yeah, we reassess", he said.
"We hope that we will have an ongoing process of making progress", CNN quoted him as saying.
Senegal, Japan: underdogs aiming for a round of 16 spot
Japan: Kawashima; Sakai, Yoshida, Shoji, Nagamoto; Hasebe, Shibasaki; Haraguchi, Kagawa, Inui, Osako. Senegal: N'Diaye, Wague, Sane, Koulibaly, Sabaly, Sarr, N'Diaye, Gueye, Niang, Mane, Diouf.
In Singapore Kim and Trump signed a joint statement in which Pyongyang committed to "work toward complete denuclearisation of the Korean Peninsula".
Also, North and South Korean officials met last week over the issue of families separated by the Korean War.
Pompeo, who has been charged with leading negotiations aimed at persuading North Korea to give up a nuclear weapons program that threatens the United States, said he would "constantly reassess" whether enough progress was being made to continue talks.
Mattis will also push for more regional security cooperation from China by pointing out that the suspension of USA military exercises with South Korea satisfies a major Chinese strategic objective, which is the real reason China has insisted so strongly on its "freeze-for-freeze" plan that made suspension of American exercises a precondition for nuclear talks with North Korea.
Trump rescinds Obama order on Great Lakes protections
It's drawing praise from groups representing offshore energy producers, and drawing fire from environmentalists. The order had also created a council to promote conservation and sustainable use of water.