The Mongol Ruler who captured the capital of the Song Dynasty and was thus emperor of all China was Kublai Khan.
Who was Kublai Khan?
Kublai Khan was the descendent of Genghis Khan who got to inherit China when Genghis Khan's empire was split up after his death.
After years of fighting, Kublai Khan was able to invade and defeat the Song Dynasty of southern China which then allowed him to proclaim himself as emperor of a unified China.
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