The clashes broke out during a police raid on a militant hideout in a mountainous area on the edge of the southern province of Sohag, some 460 kilometres south of Cairo, the ministry said in a statement.
Police seized weapons and ammunition, it added. The operation is part of "the interior ministry's efforts to confront terrorist organisations aiming to undermine security and stability" in Egypt, it said.
Attacks have largely been concentrated in the turbulent northern Sinai region, but have also taken place elsewhere across the country.
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