Pompeo, who arrived from North Korea, told Yi he wanted to fill him on his meetings with its leader, Kim Jong Un, and efforts to achieve the denuclearization of the Korean Peninsula.
After spending about five hours in Beijing, Pompeo headed for the airport to return to Washington.
The possibility of a summit between Kim and Japanese Prime Minister Shinzo Abe is also "open", Moon said, adding: "A new order is being created on the Korean peninsula".
"I hope Secretary of State Pompeo's visit to China will play a positive role toward this goal", the Chinese foreign minister said.
"We require that the USA stop such misguided actions", he pointed out, adding that the two countries should pursue cooperation "and not descend into conflict and confrontation".
Pompeo said "he agreed with Chairman Kim to hold the second US-North Korea summit at the earliest date possible", South Korea's presidential office said in a statement, although no specific time or location has yet been agreed.
Kim and Mr Pompeo agreed to arrange another summit between the Korean leader and US President Donald Trump "as soon as possible".
"We believe this has been a direct attack on our mutual trust, and has cast a shadow on China-U.S. relations", he added.
This time, Kim was satisfied with the "productive and wonderful talks" with Pompeo, according to the regime's Korean Central News Agency.
On Monday, Pompeo wrapped up his three-day East Asia tour aimed at pressing North Korean leader Kim Jong Un to give up his country's nuclear weapons and long-range missile programmes.
"The United States is continuing to act against Chinese interests, including the U.S".
He briefed Wang on his visit to the Democratic People's Republic of Korea (DPRK), voiced the US side's appreciation of China's consistent position on the Korean Peninsula and its efforts on denuclearization, and expressed a willingness to continue related cooperation.
The country's state newspaper, Rodong Sinmun, featured eight photos of the meeting on its front page, including various shots of Kim and Pompeo smiling and shaking hands - and some with Kim's sister Kim Yo Jong in attendance. According to the former official, the North Korean diplomats told him that denuclearization for them refers to a process by which the USA also reduces its nuclear weapons, possibly worldwide.
Washington and Pyongyang have sparred over the exact terms of the vaguely-worded agreement in Singapore, with the U.S. pushing to maintain sanctions and pressure against the North until its "final, fully verified denuclearisation".
In an interview with the Washington Post, she said the North could agree to dismantle Yongbyon, its signature nuclear site.
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