"For Asia, the severity of China-U.S. frictions is taking up much attention and is, to some extent, diluting attention paid to the Korean peninsula issue", it said.
The top USA diplomat met with the North Korean leader in Pyongyang for two hours before Pompeo flew to South Korea on Sunday afternoon for a two-day visit.
Although the meeting only last two hours, Secretary Pompeo tweeted afterward, "Had a good trip to #Pyongyang to meet with Chairman Kim", noting the leaders "continue to make progress on agreements made at Singapore summit".
Asked whether Xi had declined a meeting because of disagreements between the two sides, Pompeo said: "I expect they'll also raise the issues that they're happy with".
A spokesman for South Korean President Moon Jae-in made the announcement ahead of Moon's trip to Europe next week, where he will visit the Vatican and extend Kim's invitation to Pope Francis in person.
Kim and Xi have met three times in China this year as the two countries seek to fix relations frayed by tensions over the North's nuclear activities and Beijing's backing of United Nations sanctions against its Cold War-era ally.
The US should cease military contacts and halt further arms sales to Taiwan, and it should stop interfering with Chinese efforts to establish diplomatic relations with Taiwan's diplomatic allies, he said.
But the senior USA official said the United States still expected cooperation with Beijing on efforts to denuclearize North Korea, whose chief ally is China.
Pompeo met Wang and Yang Jiechi, a senior Cabinet official and former foreign minister, after talks Sunday with Kim in North Korea's capital, Pyongyang. "An announcement of a near-term summit would show that the Trump administration has again prioritized a flashy show over real substance", he said.
"Kim Jong Un expressed satisfaction over the productive and wonderful talks with Mike Pompeo at which mutual stands were fully understood and opinions exchanged", KCNA said.
Pompeo also met China's top diplomat Yang Jiechi, a Politburo member who heads the ruling Communist Party's foreign affairs commission, though remarks before reporters took a more conventional tone, even as both agreed relations faced many challenges. On that occasion, he did not meet with Kim. US officials have thus far said the penalties will remain in place until the North's denuclearization is fully verified.
The two countries have, however, been in a standoff over what the term denuclearisation means.
But, as Pompeo made his way back to Washington after three days of talks in Tokyo, Pyongyang, Seoul and Beijing, it was unclear what had been accomplished. He also urged world leaders to mediate in the crisis and find a diplomatic solution.