The visit, whose length and content have not been specified in reports, is the first by a high-ranking Chinese official to North Korea in more than a year.
During his visit, Song was widely expected to try to ease the standoff over North Korea's nuclear weapons and missile programs.
During the three-day trip, the Russian envoy will reportedly sit down for talks with his South Korean counterpart Lee Do-hoon and Deputy Foreign Minister for Political Affairs Yoon Soon-ku.
A meeting between Song and Kim Jong-un was seen as an opportunity for the envoy to deliver a letter from Chinese President Xi and discuss the North's nuclear and missile tests.
The report said Song told his hosts China wanted to "develop the traditional friendly relations between the two parties and countries" but contained no further details of what was discussed.
Over the past few months Kim and US President Donald Trump also engaged in incessant verbal spat, with the latter branding the former as "rocket man", and the North Korean leader calling Trump a "mentally-deranged dotard" in response.
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But experts doubt Song's visit will yield major breakthroughs.
Song has already visited Vietnam and Laos to inform them of the results of the congress, a typical courtesy China extends other communist countries after such important meetings. "Perhaps (the mission) will put a floor under China-North Korea relations, preventing further deterioration".
"Song is not a magician", the newspaper said in an editorial Friday. The North Korean state media quoted the Chinese diplomat as saying the CPC's position is to improve ties with the Pyongyang regime. China sent an envoy to North Korea after each of the past two party congresses, in 2007 and 2012.
It said that the United States needs "real resolve and drive to change the situation" on the Korean Peninsula, and that allowing Pyongyang to "have a sense of security is the prerequisite for resolving the peninsula nuclear issue". "If both sides insist on their own logic and refuse to move in the same direction, even if Song opens a door for talks, the door could be closed anytime".
China and Russian Federation have been against the deployment as they believe it will not do anything to ease the tensions in the region.