Egypt is battling an Islamist militant insurgency that has carried out attacks mainly in the remote Sinai Peninsula.
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.
The latest extension was to allow security forces to "take (measures) necessary to confront the dangers and funding of terrorism and safeguard security in all parts of the country."
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.