They are expected to take up the recent flurry of developments on the Korean peninsula.
At the moment, North Korea detained three USA citizens: Korean-American missionary Kim Dong-Chul, Professor Kim sang-Duk, also known as Tony Kim, who about a month teaching students at the University of science and technology in Pyongyang before his arrest in 2017, and Kim HAK-Sung, who also taught at UNCP. The businessman who once ran a hotel in the North said he had tried to steal military secrets for South Korea during a staged press conference in 2016.
The two-day visit was the second visit Kim made to China in the past 40 days.
Pompeo was also expected to return to Washington with an exact time and location for the Trump-Kim summit.
Trump has said that withdrawing USA forces from South Korea is "not on the table".
USA officials said Pompeo will also press North Korea for the release of three detained American citizens, whose imminent release Trump has been hinting at.
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The leaders of Japan, China and South Korea on May 9 agreed to cooperate for the denuclearization of North Korea, but they stressed different courses to achieve that goal.
A Trump-Kim meeting seemed a remote possibility just a few months ago when the two leaders were trading threats and insults over North Korea's development of nuclear weapons and ballistic missile tests.
Pyongyang has been making every effort possible to show that Kim is going to meet Trump from a position of strength and not out of compulsion and the travel by plane was also a part of that strategy.
Kim was accompanied to China by his sister, Kim Yo Jong, who has played a leading role in diplomatic overtures by the long-isolated country.
May 7: Kim meets Xi again in China's Dailan and calls for stronger "strategic cooperation" between the traditional allies amid shifts in the region's political environment.
Amid tranquil scenes of the two leaders chatting beside deep blue ocean waters and strolling through lush gardens, state media quoted Xi as telling Kim that China "supports North Korea to stick to denuclearization of the Korean Peninsula and supports North Korea and the U.S.in solving the peninsula issue through dialogue and consultation".
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The first summit between the three countries in nearly three years also cams after Kim made an unexpected visit to China's northern port city of Dalian for talks with Chinese President Xi Jinping. He was detained last May for alleged anti-state activities and accused of "hostile acts", Fox News reported.
"We share the view that complete denuclearization and establishment of lasting peace on the Korean Peninsula is very important to peace and prosperity of not only the Korean Peninsula but Northeast Asia", President Moon Jae-in said, thanking Japanese Prime Minister Shinzo Abe and Chinese Premier Li Keqiang for the special declaration.
In March, Kim traveled by train to Beijing, his first known trip overseas since assuming power in 2011.
A US official said that "substantial progress" has been made on plans for a summit. The venue for their summit has not been announced.
"Experts basically believe that these three were basically detained in order to serve as bargaining chips with the US for North Korea, or even, in the event of a military conflict, human shields", Kuhn reports.
South Korea's presidential office said the Chinese government notified Seoul about the Xi-Kim meeting in advance.
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A State Department official travelling with Pompeo said the USA would also be "listening for signs from North Korea that things have substantially changed" with the nation's nuclear ambitions.
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