The two met in an unannounced summit on Monday and Tuesday, in the port city of Dalian in China, just weeks after they took part in historic talks in Beijing. That strongly suggests an urgent situation has arisen, and the two leaders needed to discuss it ahead of Kim's meeting with Trump.
Hong Kong's South China Morning Post newspaper cited two unidentified sources as saying that Mr Xi had flown to Dalian on the coast east of Beijing to preside over the official launch of sea trials for China's first entirely self-built aircraft carrier.
Chinese state media said Xi reiterated China's support for a U.S.
He was also quoted as saying: "I hope to build mutual trust with the U.S. through dialogue".
"At this very moment, Secretary Pompeo is on his way to North Korea in preparation for my upcoming meeting with Kim Jong-un", Trump said. The North is now detaining three US prisoners, and early talks before the summit strongly inferred that the prisoners would be released as a deed of "good will", according to inside White House source Rudy Giuliani. "Maybe North Korea and the U.S. are thinking about making some radical concessions".
In the interview, Moon said Kim's desire for "complete denuclearisation" laid the groundwork for the future summit between the United States and North Korea, although it remained to be seen if concrete steps were agreed at the talks.
Both U.S. President Donald Trump and Kim were supposed to announce the date and place of their first summit by now.
Foley pointed out that North Korea has made numerous promises of going nuclear-free in past decades as well, with hopes of peace never actually materializing.
The two leaders "opened their hearts and had warm conversations", North Korea's state news agency KCNA reported.
While China and North Korea have always been allies, their diplomatic relationship grew rocky following Kim's rise to power in 2011.
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.
It is not clear when the meeting was planned or put together or why Dalian was chosen.
Chinese internet users posting on social media described heavy security in the city and extensive flight delays on Monday.
Throughout the day on Tuesday there was speculation on Chinese websites that a North Korean leader was in China, though China's foreign ministry said earlier it had no information and Chinese state media did not carry any reports.