It would be the Chinese leader's first official visit to North Korea since he came to power as head of the Chinese Communist Party in November 2012.
Next week Kim will meet with South Korean President Moon Jae-in, who has led a diplomatic push to engage North Korea, in the demilitarized zone between the two countries.
Russia requests Kim summit
Kim said Song's visit and the performance by the Chinese ballet troupe were the "fruition of the special intimacy and deep interest" between the two countries, according to North Korean state media KCNA.
According to the official, Song's visit was also intended as an opportunity to discuss Xi's upcoming trip to Pyongyang.
Russia has also requested a personal summit with Kim, the official said, but the North Koreans haven't responded yet.
Both countries touted their 70 years of diplomatic relations during the trip, saying their leaders "regularly exchange statements."
Old alliance rekindled
Kim purged several key officials with close ties to Beijing, including his uncle Jang Song Thaek, and angered China through its provocative missile and nuclear testing, which went against Beijing's goal of a denuclearized Korean Peninsula.
Xi hosted the young North Korean leader and his wife at a grand banquet in the Great Hall of the People.
Both men spoke enthusiastically about relations between the two countries during the visit, according to state media, with Kim quoted as saying he chose China as his first international visit to demonstrate how much he "valued (China's) friendship."
According to the state-run news agency Xinhua, Xi said he wanted to work with Pyongyang to promote relations between the two neighbors.