The regional parliament adopted a resolution urging Paris to ensure the immediate closure in Corsica "of prayer or meeting places that act as centres of radicalisation or where hateful speeches are made, creating an atmosphere that is favourable to violence."
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The resolution was adopted with a landslide, with MPs from the nationalist, left and right parties voting for, and only three Communists abstaining.
Passed at the peak of the tourist season, the text also calls for tighter security measures in areas frequented by holidaymakers.
The resolution was passed after a splinter group of the nationalist Corsican National Liberation Front (FLNC) in a statement warned militants that any attack on the island would trigger "a determined response, without any qualms".
"What the Salafists want is clearly to install in our home the politics of Daesh, and we are ready for that," the FLNC October 22 group said in a statement published in the Corse Matin daily, using another name for the Islamic State group.
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"Your mediaeval philosophy does not scare us," the statement added.
Then, addressing "Muslims in Corsica" in general, the militant group called on them to "take a stand" by denouncing radical Islamism, and urged them to inform on "disaffected youths who are tempted by radicalisation".
The group also warned the government in Paris that it would be held partly responsible for any militant attack on the island, "because it knows who the Salafists in Corsica are".
In less than two weeks IS group militants claimed four bloody assaults in France and Germany that killed nearly 90 people, wounded hundreds and left the continent on edge.
Fear of fresh violence and tensions in France have spiked since July 14, when a Tunisian man ploughed a 19-tonne truck into a crowd leaving a fireworks display in the Riviera city of Nice.
Then on Tuesday morning, two militants slashed a priest's throat during mass in northern France.
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One of the attackers had been charged over terror links, after two failed attempts to join militants fighting in Syria.
In Corsica last December, angry protesters vandalised a Muslim prayer hall and trashed copies of the Holy Quran after an assault on firefighters that was blamed on local youths of Arab origin.
"The parents abandon them, the problem is education," a 35-year-old local resident named Mehdi said at the time. "But us, we want to all live together, without a problem."
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