Pompeo's last trip to North Korea in July did not go well.
His comments came before a meeting Saturday with Japanese Prime Minister Shinzo Abe in Tokyo.
Pompeo said it was important to hear from the Japanese leader "so we have a fully coordinated and unified view".
"Well, I am really pleased for this opportunity". He said they would develop options, if not finalize, the location and timing of a second Trump-Kim summit.
Pompeo "had a good meeting with Chairman Kim today in Pyongyang", Trump said Sunday on Twitter.
Pompeo said he and Kim discussed denuclearization steps to be taken by the North and the issue of US government monitoring of those actions, which Washington sees as vital, as well as the measures the United States would conduct in return, Moon's office said.
Kim said he believed the dialogue between the two countries would continue to develop favorably "based on the deep confidence between the two leaders of the two countries", and expressed gratitude to Trump for making a honest effort to implement the agreement made at their historic June summit, KCNA said. "Thanks for hosting me and my team".
North and South Korean leaders said that the North will permanently close its missile test site and dismantle its main nuclear facility if the United States takes corresponding measures under a deal struck at the inter-Korean summit between Kim and South Korean President Moon Jai-in last month.
Moon expressed hopes that Pompeo's trip and the proposed second meeting between Kim and Trump would make "irreversible, decisive progress in terms of denuclearization as well as the peace process".
In recent weeks, US officials have pointed to a recent meeting in Pyongyang between Kim and Moon, when North Korea committed to dismantling a missile-engine-testing site and raised the possibility of doing the same at its Yongbyon nuclear-enrichment facility.
'Thank You For Choosing Me' - Atiku Reacts To Victory At PDP Primary
Mr Jonathan described Mr Abubakar as a man who has the capacity to take the country to greater heights. You have said it is not something you are going to do alone.
Nokia 7.1 Smartphone with PureDisplay & Nokia True Wireless Earbuds Launched
Alongside the Nokia 7 .1, HMD Global also took the wraps off a new pair of wireless earbuds, dubbed TrueWireless Earbuds. The device has a dual camera setup on the back, with 12MP and 5MP sensors that are capable of enabling Bothies.
This is a Big Win for Wisconsin's Dairy Farmers
In order to keep the 24-year-old deal alive, negotiators from all three countries spent the entire weekend working over the phone. But now, things such as breakfast cereal swimming in milk have been replaced by fast-food egg sandwiches or a bagel at work.
After a previous visit to Pyongyang in July, Pompeo had said the two foes made progress on key issues - but within hours of his departure the North condemned "gangster-like" demands from the USA, raising questions over how much the two sides really saw eye to eye.
"A verifiable shutdown of Yongbyon would make it harder for North Korea to further expand its fissile stockpile" and "create momentum for further action-for-action steps, and help buy time for the long and difficult steps on the road toward denuclearization", Daryl Kimball, executive director of the Arms Control Association, said in a statement, adding that an end-of-war declaration would also "ease tensions, build confidence, and in no way adversely affect the very strong U.S".
The visit was Pompeo's fourth to North Korea.
The US and Japan have pushed for the North to compile and turn over a detailed list of its nuclear sites to be dismantled as a next step in the process; the North has rejected that.
Trump has appeared eager to meet Kim again, even though the two sides are seen far from narrowing their differences.
"South Korea seems overly eager to improve relations and offer benefits to North Korea without requiring commensurate progress in reducing the North Korean security threat", said Klinger. Kim's regime has said it wants to focus on more than just its nuclear program, and that it expects the U.S.to show some flexibility with its demands. The war concluded with an armistice but no peace treaty.
North Korean Foreign Minister Ri Yong-ho told the United Nations General Assembly at the end of last month that "coercive" sanctions were lethal to trust-building between the two nations, and that without trust "there is no way we will unilaterally disarm ourselves first".
With talks largely deadlocked, at the heart of this round of negotiations is a debate over what the US should demand from North Korea and what it is willing to give in exchange.
He visited Tokyo on Saturday and will head to Beijing before returning to the US on Monday.