The mother of an American hostage being held by the Islamic State in Iraq and Syria released an emotional video appeal to his captors on Wednesday. Shirley Sotloff, the mother of the 31-year-old freelance journalist Steven J. Sotloff, addressed her plea directly to Abu Bakr al-Baghdadi, the leader of ISIS and the self-declared caliph of the Muslim world.

Ms. Sotloff addresses Mr. Baghdadi as caliph, a title he bestowed on himself a few months ago, and calls on him to exercise his right to show clemency and follow the example of the Prophet Muhammad as previous caliphs did.

“I am sending this message to you, Abu Bakr al-Baghdadi al-Quraishi al-Hussaini, the caliph of the Islamic State. I am Shirley Sotloff. My son Steven is in your hands,” she begins. “You, the caliph, can grant amnesty. I ask you please to release my child,” she continues. “I ask you to use your authority to spare his life.”

Mr. Baghdadi — an Iraqi national who was jailed briefly by American forces in 2004 — declared a caliphate this year after his group captured a significant chunk of territory in Iraq. His claim to authority has not been recognized by most Muslims. In addressing Mr. Baghdadi as caliph of the Muslim world, Ms. Sotloff’s appeal is almost certainly the first time a non-Muslim has acknowledged his authority.