Eight militants were killed in exchange of fire with army in Shiekh Zwayed city, while three others were killed in Al-Arish city, military spokesperson Brigadier General Mohamed Samir said in a statement.
He said that four tunnels used by militants to hide from the army were also discovered and destroyed.
The army operations are part of the retaliation campaign launched by the army to avenge the last month attack that killed 12 soldiers in North Sinai.
Senior officer Hisham Mohamed Mahmoud was killed yesterday after three gunmen opened fire on him in front of his house after the Friday prayer, Samir said.
Last month, unknown gunmen assassinated another senior army officer; Brigadier General Abdel Raga'e; near his house in Obour City, about 35 kilometers north-east of Cairo.
Egypt has witnessed a series of terrorist attacks which targeted policemen, judges and military personnel in different parts of the country.
Since the 2011 revolution that topped ex-president Hosni Mubarak, North Sinai, which is the base of a number of extremist outlaw groups, has witnessed a number of terror attacks.
Over 700 security personnel have been reported killed since then.
The military has launched security campaigns in the area, arrested suspects and demolished houses that belong to terrorists, including those facilitating tunnels leading to the Gaza Strip.
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