No casualties were reported in the fighting, Ahram Online reported.
One battle erupted when a car fired on a checkpoint outside Sheikh Zuwayed, which is near the border with the Gaza Strip.
The second incident, in the Bedouin town, began when militants in a school building reportedly fired on army forces. The army surrounded the school with armored vehicles. Gunfire shattered the windows of homes in the neighborhood.
Some 78 suspected militants have been killed during recent operations by security forces in the Sinai, Col. Ahmed Ali, a military spokesman, said Friday. Some 203 people have been arrested.
Attacks on the military have been on the rise in the Sinai since the ouster of President Mohamed Morsi.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Exploding whale video goes viral on Internet