At the same time, the United States and China are cooperating on efforts to pressure North Korean leader Kim Jong-un to give up his country's nuclear weapons and long-range missile programs.
Mr Moon spoke of the imminent travel plans of the North Korean and Chinese leaders during a Cabinet meeting a day after US Secretary of State Mike Pompeo travelled to North Korea, but did not elaborate further.
Pompeo landed in Pyongyang on Sunday morning to meet Kim after visiting Japanese Prime Minister Shinzo Abe on Saturday in Tokyo. "We have great concerns over the actions that China has taken and I look forward to having the opportunity to discuss each of those today because this is an incredibly important relationship".
After Seoul, Pompeo ends his trip Monday in China, North Korea's political and economic lifeline.
Kim is ready to invite worldwide experts to inspect the Punggye-ri nuclear test site, which Pyongyang invited global journalists to witness being demolished in May, according to Pompeo.
The visit was Pompeo's fourth to North Korea.
Stressing that these moves have directly impacted on the mutual trust and cast shadows on the prospects of China-U.S. relations, Wang urged the United States to stop making negative remarks immediately.
In a summit in April, the leaders of South and North Korea agreed to cooperate in declaring an end to the war this year, saying that they will seek multilateral talks involving the USA and possibly China.
Last month, Mr Putin invited Mr Kim to visit his country but details about where and when the talks could take place have yet to be decided. Chairman Kim said he's ready to allow them to come in.
Pompeo replied that it was "important that we listen to each other, work through and find constructive solutions so we can find a good outcome for both our countries".
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Pompeo did not specify when the summit will be or if Pyongyang has been ruled out as a location.
The trip was the latest turn in a diplomatic saga that saw Trump and Kim threaten each other with nuclear war a year ago only for them to hold their historic summit in Singapore.
Trump met with Kim in Singapore in June and - at the time - announced that the two countries are set to "start a new history".
In Pompeo's last trip to Pyongyang in July, North Korea denounced him for making "gangster-like demands".
When asked for a date on the inspection, Pompeo responded: "As soon as we get it logistically worked out".
Chinese State Councilor and Foreign Minister Wang Yi talks with U.S. Secretary of State Mike Pompeo before a meeting at the Diaoyutai State Guesthouse in Beijing, China October 8, 2018. Thank you for hosting, President Trump sends his regards.
Since Trump and Kim met, US-North Korea relations have stalled.
DPRK is the acronym for the North's official name, the Democratic People's Republic of Korea.
At a meeting in Beijing Monday, Pompeo said the White House has "great concerns about China's actions".