When Kutalmish died in 1064, Suleiman fled with his three brothers into the Taurus Mountains and there sought refuge with Turkmen tribes living beyond the borders of the empire.
Kui Qutalmish aastal 1064 suri, põgenes Suleiman koos oma kolme vennaga Tauruse mägedesse, kus ta otsis varjupaika türkmeeni hõimudelt, kes elasid väljaspool impeeriumit.