However, Chinese 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".
Trump and Kim are expected to meet later this month or early in June for talks that would have been almost unthinkable a year ago, when the two mercurial leaders were trading barbs and Pyongyang tested a barrage of missiles. "The primary topics will be Trade, where good things will happen, and North Korea, where relationships and trust are building".
"President Trump and President Xi agreed on the importance of continued implementation of sanctions on North Korea until it permanently dismantles its nuclear and missile programs", the statement said.
China's top diplomat, Wang Yi, met with Kim in Pyongyang last week, the first trip there by a Chinese foreign minister since 2007. Broadly speaking, recent developments between North and South Korea have been met with widespread optimism and praise from the South Korean public.
China is the only major ally of North Korea, though in recent months, trade between them has declined sharply, as Beijing uses economic United Nations sanctions in response to nuclear bomb tests and ballistic missiles of the North, writes CBSnews.
In an unprecedented meeting at the demilitarized zone separating the two countries, Kim became the first North Korean leader to step into South Korean territory since 1953.
It is not known how long the Xi-Kim meeting had been planned or why Dalian was chosen.
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Some analysts have said China also wants to keep its influence on North Korea amid diplomatic efforts by Seoul and Washington to ease tensions on the Korean Peninsula.
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".
But after months of saber-rattling, and a historic summit between Kim and the South Korean president, Moon Jae-in, the mood is decidedly more upbeat, and Trump has said a date and location are already set - though he did not divulge any specifics.
The March meeting was Kim's first worldwide trip since he assumed power in 2011 following his father's death, and was seen as a warming of ties between the two fractious allies. Indeed, despite the short turnaround between Xi and Kim's meetings, there was a lot to catch up on.
Speculation about Kim's visit to China started when security in Dalian, located close to the China-North Korea border, was increased and Kim's private jet was spotted at the airport of Dalian. The venue for their summit has not been announced.
Shortly after the May 8 meeting was announced by Chinese state media, Trump said on Twitter that he would speak to his "friend" Xi about North Korea.
His trip was kept secret until he returned to North Korea. "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.