The announcement came after the jihadists claimed a series of attacks, including a shooting near a monastery this week and twin church bombings on April 9 that killed dozens.
Among the jihadists killed was “one of the prominent leaders of the so-called Ansar Beit al-Maqdis, the head of the religious affairs committee in the group,” the military said, without saying when the strikes occurred.
Ansar Beit al-Maqdis was the name used by the jihadists in the Sinai before they pledged allegiance to the Islamic State group in November 2014.
The jihadists have killed hundreds of soldiers and policemen since the army overthrew Islamist president Mohamed Morsi in 2013.
The military has killed several of their top leaders, but the extremists have increasingly expanded their attacks from the Sinai to other parts of Egypt, especially against Christians.
The April 9 church bombings in the cities of Tanta and Alexandria followed a December suicide bombing in a Cairo church that killed 29 people, also claimed by IS.
On Wednesday, the interior ministry said security forces killed a gunman suspected of killing a policeman and wounding three others near St Catherine’s monastery in south Sinai the day before.
IS, which claimed the shooting, has threatened more attacks on Coptic Christians, who make up about 10 percent of Egypt’s population of more than 90 million people.