Which empire did the First Crusade primarily fight against?

Which empire did the First Crusade primarily fight against? The crusaders primarily fought the Seljuk Turks.

The First Crusade began after Byzantine Emperor Alexios I Komnenos appealed for help against Turkish forces that had seized much of Byzantine Anatolia. These forces were associated especially with the Seljuk Sultanate of Rum, a branch of the wider Seljuk world. The crusaders therefore encountered Seljuk armies and governors across Anatolia and northern Syria.

The campaign was not a single war against one perfectly unified state. Seljuk power was divided among regional rulers, and the crusaders also fought other Muslim forces, including the Fatimid Caliphate in Egypt. The Fatimids controlled Jerusalem when the crusaders captured it in 1099, which explains why that answer can seem plausible but is not the best answer to this question.

The Abbasid caliph in Baghdad remained an important religious authority but was not the main military opponent. The Ottoman Turks appeared centuries later, beginning in the late thirteenth century, so they cannot be the answer.