U.S. terrorist-tracking organisation SITE reports said on its website: "The Islamic State's (IS) 'Amaq News Agency reported that the group is responsible for the attack near St. Catherine's Monastery in south Sinai".
The attack, which plunged the country into mourning and marked one of the bloodiest days for the country's Christian minority in decades, was also claimed by the Islamic State.
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A state of emergency already in place in northern Sinai has failed to halt near-daily attacks against police and security forces by Daesh in the volatile area. This caused the militants to flee the scene; one of them left his gun and some ammunition.
Three other officers were wounded in Tuesday's attack in South Sinai province at a checkpoint near the ancient site, the ministry said.
The Islamic State claimed responsibility for the attack and:bombings at two Coptic Christian churches on Palm Sunday that killed 45 people.
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Egypt has been fighting an Islamist insurgency which has targeted Christians and Egyptian security forces on both the mainland and in the Sinai. Police found an automatic weapon and ammunition, the ministry said.
Egypt's Christian minority comprises about 10% of the predominantly Muslim country of 92 million people.
The statement added that the council stood with the country's minority Coptic Christians and condemned the attacks on their churches. Visitor numbers have yet to recover since the 2015 downing of a Russian passenger jet after it took off from Sharm El-Sheikh killed all 224 on board.
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Despite the state of emergency in Egypt and despite the efforts by the Egyptian government to fight against ISIS, the murderous terror group proved that it can strike in the Southern Sinai not too far away from popular tourist destinations along the shores of the Red Sea.