Sentence:  As the rulers of the old Roman capital, the capital of the Caliphs, Baghdad, and the Holy Cities of Mecca, Medina and Jerusalem they had ample support to convince a medieval audience of their claim to universal <WSD>suzerainty</WSD>. But even among Muslim states, their imperial claims did not go unchallenged. The Safavid and Mughal Empires raised similar claims to <WSD>suzerainty</WSD>. 
Meaning of the word marked with <WSD> tags:  A relation between states in which a subservient nation has its own government, but is unable to take international action independent of the superior state; a similar relationship between other entities.