The Islamic State group's Egyptian affiliate, Ansar Beit al-Maqdis, claimed in a video released Monday the killing of a police officer whose body was found almost two weeks ago.
Egyptian troops found the body of Ayman al-Desouky, who had been kidnapped from near the town of Rafah on the border with the Gaza Strip, during a search operation in North Sinai on January 13.
In the video released on its Twitter account, Ansar Beit al-Maqdis (Partisans of Jerusalem) said its militants abducted Desouky and later executed him.
The footage shows gunmen dragging a policeman out of a car at a checkpoint manned by militants wielding machineguns and rocket-propelled grenades.
It then shows a militant shooting the blindfolded and handcuffed officer in the head three times.
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Prior to the shooting, the video titled "We swear to avenge" shows riot police arresting female protesters at Cairo's Al-Azhar University, the prestigious seat of Sunni Muslim learning.
In November, Ansar Beit al-Maqdis, the deadliest militant group in Egypt, pledged its allegiance to the Islamic State jihadist group, which has captured large chunks of territory in Syria and Iraq.
The group, which is based in the Sinai Peninsula, has claimed a string of killings of what it says were informants to the Egyptian and Israeli security forces.
It has also claimed a late October attack on troops near North Sinai's provincial capital of El-Arish that killed 30 soldiers.
In response to that attack, the authorities imposed a state of emergency in parts of North Sinai, which was extended by another three months on Sunday.
The army has poured troops and armour to fight a dogged insurgency on the peninsula that has grown since then army chief and now President Abdel Fattah al-Sisi ousted his Islamist predecessor, Mohamed Morsi, in July 2013.
Jihadists like Ansar Beit al-Maqdis say their attacks targeting security forces are in retaliation to a government crackdown against Morsi's supporters that has left hundreds dead.