Spokesman Col. Tamer el-Rifaai said that forces also arrested five militants and 680 others including "criminal elements" and people suspected of supporting militants.
He spoke at a press conference in the presence of senior military and Interior Ministry officials.
El-Rifaai also said that forces found and destroyed hundreds of militant hideouts, targets and explosive devices.
The casualty figures couldn't be independently verified as journalists and independent investigators are banned from accessing the turbulent Sinai region.
The operation involves land, sea and air forces.
Authorities are not saying how long the operation will last.
Earlier today, the army said that airstrikes in the Western Desert destroyed 10 SUVs laden with weapons and ammunition.
Egypt has for years been struggling to contain the insurgency concentrated in north Sinai, spearheaded by a local affiliate of the Islamic State group.
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