Seven "terrorists and criminals" were arrested after the shootout, which took place yesterday in North Sinai, an army statement said, without specifying exactly where the fighting occurred.
The military's announcement on its official Facebook page comes after a suicide car bombing at a military checkpoint in North Sinai killed at least 30 troops on Friday.
The bombing was one of the deadliest attacks targeting security forces since the army ousted president Mohamed Morsi last year.
The authorities have imposed a three-month curfew in some parts of North Sinai in response to the bombing, which President Abdel Fattah al-Sisi said was carried out with the help of "external powers".
The army has poured troops and armour into North Sinai to crush an insurgency that has surged since Morsi's ouster.
Jihadists, who have killed scores of security personnel, say their attacks are retaliation for the wide-scale government crackdown against Morsi's supporters.
The crackdown has left at least 1,400 people dead and more than 15,000 jailed.
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