Amaq reported that Adnani was killed "while surveying the operations to repel the military campaigns against Aleppo".
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Islamic State holds territory in the province of Aleppo, but not in the city where rebels are fighting Syrian government forces.
Amaq did not say how Adnani was killed. Islamic State published a eulogy dated Aug. 29 but giving no further details.
Recent advances by the US-backed Syrian Democratic Forces, an alliance of Kurdish and Arab militias, and by Syrian rebels backed by Turkey, have made inroads into Islamic State holdings in Aleppo province, cutting them off from the Turkish border and supply lines along it.
Iraq said in January that Adnani had been wounded in an air strike in the western province of Anbar and then moved to the northern city of Mosul, Islamic State's capital in Iraq.
Adnani is a Syrian from Idlib, southwest of Aleppo, who pledged allegiance to Islamic State's predecessor al Qaeda more than a decade ago and was once imprisoned by US forces in Iraq, according to the Brookings Institution.
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He has been the chief propagandist for the ultra-hardline extremist group since he declared in a June 2014 statement that it was establishing a modern-day caliphate spanning large swaths of territory it had seized in Iraq and neighbouring Syria.
Adnani has often been the face of the Sunni militant group, such as when he issued a message in May urging attacks on the United States and Europe during the holy month of Ramadan.
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