The security operation launched on Friday involves troops from the Egyptian air force, navy and army as well as the police and border guards.
Israeli and Egyptian officials refused to confirm the report by the New York Times.
The members of the Sinai Province of the Islamic State are fueled by a never-ending sense of divine mission.
Sisi ordered armed forces to end the insurgency within three months after an attack on a mosque in North Sinai last month killed more than 300 people.
Army says monitoring system detected rockets being launched but later admits sirens were false alarms.
Sisi gives generals three months to cleanse the Sinai Peninsula of jihadist terrorists.
“We need to act together to eradicate terrorism everywhere and anywhere.”
In the wake of the weekend's bloodbath in Egypt's Sinai, Saudi crown Prince says terror tarnishes Islam's reputation.
ISIS's motives for the attack are both strategic and ideological.
"This attack doesn't relate to any religion," one person wrote on Facebook. "It belongs to hatred, dehumanization, evil and disgrace."