Tulunid rulers aimed to rule Egypt without challenging the Abbasid Caliphate.

Evidence

The establishment of the Tulunid state, and its revival and continuance by subsequent rulers, mark a significant change in the history of medieval Egypt. Ibn Tulun, the Ikhshid and Kafur were all foreigners in Egypt; their aims were personal or at most dynastic, and were limited in both territorial extent and political content. As Sunni Muslims, they had no desire to withdraw from the Islamic oecumene headed by the Caliph, still less to challenge the Abbasids for the Caliphate itself. — Bernard Lewis, From Babel to Dragomans, 374