After France and Britain had called for a ceasefire, Israel and Egypt continued with heavy fighting in which 231 Israeli soldiers, many of them reservists, lost their lives.
The security operation launched on Friday involves troops from the Egyptian air force, navy and army as well as the police and border guards.
Apart from Sinai, the Egyptian army said the operation would also cover parts of the Nile Delta and the Western Desert.
A recent New York Times report left many questions unanswered: find them here.
Sisi gives generals three months to cleanse the Sinai Peninsula of jihadist terrorists.
"The air force has over the past few hours eliminated a number of outposts used by terrorist elements," the army said.
The Islamist insurgency in the Sinai peninsula has grown since the military overthrew President Mohamed Mursi of the Muslim Brotherhood in mid-2013 following mass protests against his rule.
Violence against police in Egypt's Sinai Peninsula have increased since the 2013 ouster of Morsi.
Security forces also killed 15 people and arrested seven others during a raid which targeted "highly dangerous terrorists" in the central Sinai area.
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