US officials have been pressing Kim to free the three remaining American detainees as a gesture of sincerity before the summit, the first-ever meeting of sitting USA and North Korean leaders.
Kim held his first summit with Xi in March in Beijing, marking the first meeting since Kim took power in late 2011.
Pompeo reportedly left Joint Base Andrews in Maryland on Monday, with two reporters who were prohibited from reporting on their trip until after Trump's announcement on Tuesday.
However, state broadcaster CCTV quoted Xi as saying 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".
Kim said "Comrade General Secretary and I have carried on this fine tradition to hold the historic meeting with fruitful outcomes, and promoted the unprecedentedly vigorous development of the DPRK-China relations", he said.
China is likely trying to insert its interests into ongoing inter-Korean talks and shape Kim's message to President Donald Trump when the two meet.
The talks come amid a flurry of diplomacy on the Korean Peninsula, including a landmark summit in late April between Kim and South Korean President Moon Jae-in.
China is North Korea's only major ally but trade has plummeted in recent months because Beijing is enforcing United Nations economic sanctions, following ballistics missile tests in North Korea.
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"If Japan-North Korea relations are normalized, that would greatly contribute to peace and security in Northeast Asia beyond the Korean Peninsula", he said in written answers to questions submitted by the newspaper.
Pompeo told reporters aboard his plane that his first visit was to test the seriousness of North Korea's pledges to South Korea on easing tensions.
In response, North Korea denounced the Trump administration's escalation of demands by warning that Washington must not mistake "our will to achieve peace" on the Korean Peninsula for "weakness".
In exchange for a revised peace treaty, South Korea has agreed to work in conjunction with the North to denuclearize the peninsula, disarming one of the most risky regions in the world in terms of atomic power and political instability.
For his part, Kim said both the DPRK-China friendship and the Korean Peninsula situation have undergone meaningful progress since March this year.
His trip was kept secret until he returned to North Korea.
It was not known how long the Xi-Kim meeting had been planned or why Dalian was chosen.
Media reports Tuesday said Chinese President Xi Jinping may have met with a high-ranking North Korean official in the Chinese port city of Dalian amid tight security and the spotting of a North Korean airliner at the city's airport. "This meeting is one that carries the will of President Trump and State Affairs Commission Chairman Kim Jong Un", she said, using Kim's formal title.