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8 year oldIn a statement distributed by the group's supporters, Amaq News Agency reported that Abu Muhammad al-Adnani died in the province of Aleppo.
He was "martyred while surveying the operations to repel the military campaigns against Aleppo", it said.
Adnani was known for his calls for lone-wolf attacksin the West.
One of the group's founder members, he is also said to have masterminded attacks in Europe and elsewhere.
Islamic State group - the full story
The statement did not say how Adnani, who had a US bounty of $5m (£3.82m) on his head, was killed.
But a US defence official said US-led coalition forces had carried out an air strike on Tuesday in Syria targeting a "senior leader" from IS in al-Bab in Aleppo province.
"We are still assessing the results of the operation at this time," he added.
Adnani's death comes at a time when IS is suffering military reverses in both Syria and Iraq.
He was last heard in an audio message in May urging Muslims to carry out attacks in the West.
Adnani was born Taha Sobhi Falaha in the northern Syrian town of Banash in 1977.
US officials say he was one of the first foreign fighters to oppose the presence of US-led forces in Iraq after the 2003 invasion.