Moon also said the North will "permanently dismantle" its missile engine testing site and launch platform in the northwestern town of Tongchang-ri in the presence of experts from "concerned countries".
In response to a question on USA accusations that China was meddling in Washington's domestic affairs and elections, Foreign Ministry spokesperson Lu Kang on Tuesday asserted that such finger pointing is "creating something out of thin air".
Wang, the foreign minister, made clear that China was most concerned about recent US moves to improve ties with the democratically run island of Taiwan, which Beijing considers a province.
In their later meeting, Yang expressed Chinese frustration with Washington while avoiding specifics, telling Pompeo relations are "facing challenges".
This version of the story corrects 4th paragraph to make clear that Washington has been seeking inspection of Yongbyon.
Pompeo did not say when inspectors would be allowed to Punggye-ri, and the State Department did not respond when asked if they would be Americans or others from worldwide nuclear bodies.
Pompeo told a reporter travelling with him on Monday that "we made significant progress".
The first-ever summit between United States and North Korean leaders was held in June this year - a meeting critics say resulted in only a vague commitment by Kim towards denuclearization.
Since the summit, the archbishop said he has met with Francis.
The president of the Korean Bishops conference, Archbishop Hyginus Kim Hee-Joong, was present at a dinner for the South Korean delegation in Pyongyang last month, during the third summit between Korean leaders.
KCNA said: "Together with Mike Pompeo, Kim Jong-un appreciated the positively developing situation on the Korean peninsula, explained in detail the proposals for solving the denuclearisation issue and matter of concern of both sides and exchanged constructive opinions".
"As soon as we get it logistically worked out, Chairman Kim said he's ready" to "allow them to come in", and once the arrangements are made "we'll put them on the ground", Pompeo said. He and Biegun both said they expected meetings at the working level to begin soon and become quite frequent before the next summit. "We're talking about three or four different locations, timing won't be too far away".
He also emphasized the possibility of future meetings between North Korea, Japan, China and Russian Federation.
The first lady of South Korea, Kim Jung-sook, participated in the Mass with Korean bishops as a part of the festivities.
Pompeo, however, played down the differences.
"I've never been involved in an global discussion where there weren't differences of view, not only between governments but inside of governments", he said. In Beijing, Pompeo met his Chinese counterparts to discuss maintaining sanctions, although unrelated disputes between the two countries spilled into public view and he didn't meet with President Xi Jinping. In response Mr. Pompeo said: "The issues that you characterised, we have fundamental disagreements".
He also expressed gratitude towards Trump for making a honest effort to implement the agreements that were made in their previous summit in June. It has not taken any steps to halt nuclear weapons or missile development.
The US is pushing for a "final, fully verified denuclearisation" but North Korean Foreign Minister Ri Yong-ho told the United Nations general assembly in September there was "no way" his country would disarm first as long as tough US sanctions remained against his country.
In South Korea, Pompeo appeared alongside President Moon Jae-in, who said the world wanted to know the results of the Pyongyang meeting, "so if the secretary can disclose the results, please tell us".