BAGHDAD—Islamic State reasserted its authority over the Iraqi city of Fallujah on Sunday after clashes with local Sunni tribesman that showed the first signs of serious resistance to the extremist group’s two-year rule of the city.

The militants detained up to 180 men after the fighting ended late Saturday, local officials said, leading to fears among the city’s exiled leadership that the insurgency will severely punish anyone suspected of participating in the brief show of defiance.

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