Army says it launched raids and air attacks in Bir al-Abed, Rafah and Sheikh Zuweid, targeting ‘terrorist hideouts’.
Armed groups were planning attacks during the Islamic holiday of Eid al-Fitr, which started on Sunday, government says.
Army also detained 61 criminal suspects and detonated 376 explosive devices during month-long raids.
Interior ministry says security forces exchanged fire with fighters after storming their hideout in El-Arish.
Suicide attack follows discovery of four headless bodies in the conflict-wracked peninsula a day earlier.
Four gunmen also killed in the attack on police near the regional capital El Arish.
Rights body reports abuses, including torture and extrajudicial killings, as it calls for halt to military aid to Cairo.
Army says it also confiscated firearms and improvised explosive devices from fighters in the restive peninsula.
About 100 suspects were arrested and more than 30 cars and scooters were confiscated or destroyed, military says.
In a statement on Tuesday, the Egyptian army said it killed 59 insurgents and arrested 142 more.
Army spokesman said more than 1,200 explosives devices, 1,900 vehicles were destroyed as part of operation ‘Sinai 2018’.
The announcement comes as the government continues to battle armed groups in the desert region.