A similar incident took place on Sunday when two men in a four-wheel-drive vehicle opened fire on a police station in the city. Police fired back but the men escaped, the source said.
The military launched an operation against militants in the area after the killing of 16 Egyptian border guards on Aug 5.
Disorder has been spreading in North Sinai, a region awash with guns that feels neglected by the central government since the overthrow of President Hosni Mubarak last year in a popular uprising. Mubarak's government had worked closely with Israel to secure the border region.
Egyptian President Mohamed Mursi, who took office in June, has promised to restore stability.
On Sunday, Egyptian soldiers killed five Islamist militants after storming their hideout near the border with Israel, security sources and eyewitnesses said.
The troops tracked down the militants in the settlement of al-Goura, about 15 km (nine miles) from the frontier, as they searched for those responsible for the deaths of the 16 border guards.
Four of the militants were Egyptian and one was Palestinian, security sources said on Monday.
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The Camp David peace treaty of 1979 had turned the Sinai into a demilitarised zone. The region has - ethnically - a distinct identity from rest of Egypt. Having been neglected for decades by Cairo, the social grievances of the Bedouins are countless. They resort to smuggling to make a living and fight government forces, if they happen to be deployed to the area.