Kim held an unprecedented summit with US President Donald Trump in Singapore in June, and pledged to work toward denuclearisation of the Korean peninsula.
Also on Monday, South Korean President Moon Jae-in said he expects Kim to travel to Russian Federation and for Chinese President Xi Jinping to visit North Korea soon amid a global diplomatic push to resolve the nuclear crisis.
Wang's remarks made clear that China is most concerned about United States moves to improve ties with Taiwan.
"We will make - we will figure it out and make it work", Pompeo told his greeter.
"Separately from the second U.S".
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.
Meanwhile, in Washington, foreign relations experts noted that with 90 percent of North Korea's exports going through China, Beijing is the one calling the shots.
"As I've said about a thousand times, you've got no rockets flying, you've got no missiles flying, you have no nuclear testing, you have nuclear closings, closing up different areas of North Korea".
"The issues that you characterized, we have a fundamental disagreement", Pompeo said.
Two of the five people on the American side of the meeting table dealt with North Korea - new special representative for North Korea Stephen Biegun and National Security Council adviser Allison Hooker - reflecting Pompeo's desired focus.
Pompeo said this could happen "as soon as we get it logistically worked out", adding: "Chairman Kim said he's ready to allow them to come in".
Although that meeting, proposed by Mr Kim's father, Kim Jong Il, never materialised, the invitation to Pope Francis is the North's latest diplomatic initiative this year.
Moreover, Chinese officials signaled the discord undermines efforts to cooperate on North Korea, making the US bid to disarm Kim's regime even less likely.
Mr. Lu's response tailed Mr. Pompeo's Asia visit, which took him to Japan, North Korea and China.
He came away from it saying the two sides had made progress, only for North Korea to denounce him for making "gangster-like" demands and raising "cancerous" issues.
Things didn't go much better a day later in Beijing, where Pompeo had the bad fortune of being the first senior USA official to visit the country since a blistering speech on China last week from Pence.
North Korea entered talks with the US and South Korea earlier this year, saying it's willing to negotiate away its advancing nuclear arsenal. The Vatican insisted at the time that a papal visit would only be possible if Catholic priests were accepted in North Korea.
Pompeo did not have a scheduled meeting with Chinese President Xi Jinping, a fact that a senior U.S. State Department official on the trip said was not unusual, even though top U.S. officials often meet Chinese heads of state on visits.