The 21-year-old had jumped from the moving bus after the explosion and was likely kidnapped by militants who shot him and dumped his body on the side of the road, they said. One of the wounded in the bus attack was a civilian, the rest were conscripts.
The blast on the outskirts of el-Arish, northern Sinai's provincial capital, came amid a counterinsurgency operation by Egypt's military and police in the volatile desert region.
The attack comes as Egypt's military presses its largest offensive in years against militants in Sinai in response to attacks the army says have killed more than 100 policemen and soldiers since the July coup that ousted Islamist President Mohammed Morsi from power.
The deadliest attack took place August 19 when unidentified gunmen pulled 25 police conscripts off minibuses and shot them dead on the side of the main road linking Rafah to el-Arish.
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A statement purportedly released by the Sinai-based Islamic militant group Ansar Jerusalem late yesterday said the military had killed seven civilians, among them four children, in the town of Sheikh Zuweyid in northern Sinai during a military operation there on Friday.
It said the children, aged one to seven years-old, died from "tank bombardment." The statement, which listed the names of those allegedly killed, said a widowed mother and another woman also died in the military assault.
"This heinous massacre committed by the Egyptian army in this town is conclusive evidence of what we said earlier, which is that the goal of the army in this operation is the forced displacement of people in Sinai from the Zionist border region," the statement said.