Photos carried by the official Rodong Sinmun newspaper showed Chinese and North Korean officials in a massive banqueting hall with a mural of Kim and Xi shaking hands decorating one wall.
"Exchanged in earnest at the meeting were profound views on the important matters of mutual concern. and the global situation", the KCNA said.
As he accorded warm hospitality to Song, Kim remembered his recent visit to China.
During the meeting, Kim extended his greetings to General Secretary of the CPC Central Committee Xi Jinping and welcomed the Chinese art troupe headed by Song that will attend the "Spring of April" International Friendship Art Festival held in Pyongyang.
It's yet another sign of Kim's supposed willingness to improve global tensions, with planned meetings with South Korean officials and Donald Trump.
He said that the visit of the Chinese art troupe to the DPRK aims to implement the consensus, enrich the China-DPRK friendship, promote exchanges and cooperation between the two parties and enhance cultural and artistic exchanges between the two countries.
That contrasts with Song's last visit to Pyongyang last November, when he was sent as Xi's special envoy to discuss the outcome of China's 19th Party Congress.
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KCNA also issued a rare separate report on Kim's wife, Ri Sol-ju, who attended a performance by the Chinese art troupe earlier on Saturday.
Song and Kim also exchanged their views on deepening bilateral relations, the KCNA said, with Kim saying he would develop their friendship into a "fresh phase of development".
Jeong Se-hyun, a former unification minister of South Korea, said Song's visit might have helped to strengthen Beijing's claims to a seat at the table in any negotiations of a formal peace treaty on the Korean peninsula.
"North Korea is using a hedging strategy", said Boo Seung-chan, a research fellow at the Yonsei Institute for North Korean Studies in Seoul.
North Korea's relationship with its sole ally during the 1950-1953 Korean war had strained when China pushed United Nations to punish Pyongyang for its nuclear weapons programme.
"First Lady Ri Sol Ju enjoyed a ballet choreodrama "Giselle" given by the National Ballet of China", KCNA reported, adding she held "friendly talk" with the guests ahead of the performance.