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The Associated Press quoted security officials as saying witnesses saw between eight and 10 attackers, dressed in military uniforms and wearing masks. The vehicle was traveling from the nearby province of Bani Suief.
Security forces launched a hunt for the attackers, setting up dozens of checkpoints and patrols on the desert road.
Christians make up around 10 percent of Egypt's mostly Muslim population of 83 million. They have long faced discrimination, but in recent years they have found themselves increasingly targeted by Islamist extremists.
Experts told NBC News last month that the violence leveled against them was "the worst it has ever been."
Steven A. Cook, a senior fellow at the Washington-based Council on Foreign Relations, said: "They have never been targeted in the way that they are now. Egypt is extremely dangerous for Copts in ways it hasn't been dangerous before."
On Palm Sunday, bombers targeted two churches in different cities, killing at least 44 people. ISIS claimed responsibility for both attacks. At the time, officials said one of the bombers belonged the same terrorist cell that killed 30 people in December when it blew up a chapel next to the country's main Coptic Christian cathedral.