Two Egyptian soldiers were killed on Wednesday in North Sinai, hours after a speech by Defense Minister Abdel Fattah al-Sisi called for mass rallies on Friday against "violence and terrorism."
A car bomb also exploded near a police training facility in the Sinai Peninsula, state television reported Wednesday, claiming three militants died in the blast.
The incident marks the first car bomb explosion in the region since President Mohamed Morsy's overthrow on 3 July.
Nile TV said the explosion took place in Arish, in North Sinai, where violence by Islamist militants has escalated since Morsy was deposed. The channel gave no further details.
Militants usually strike at night but the two soldiers were killed in separate, daylight attacks in the port town of El Arish.
Militants in North Sinai, a lawless desert region near Egypt's border with Israel and the Palestinian Gaza Strip, have attacked security checkpoints and other targets on an almost daily basis since 3 July.
On Monday, Health Ministry said that victims killed in Sinai during attacks by gunmen since the ouster of President Morsy has reached 21 including seven civilians and 14 armed forces and police personnel.
Army sources estimate there are around 1,000 armed militants in Sinai, many of them nomadic Bedouin tribesmen, divided into different groups with varying ideologies or clan loyalties, and hard to track in the desert terrain.