The fighting broke out in the area of Al-Wifaq, in northern Sinai, after militants tried unsuccessfully to blow up a police vehicle with explosives.
Clashes between the gunmen and the army were ongoing, the sources said, with Bedouin elders trying to negotiate a ceasefire.
There no immediate reports of casualties.
The restive Sinai peninsula, home to Egypt's luxury Red Sea resorts, has been hit by a surge of violence since Morsi's ouster on July 3, with militants killing a police officer early on Friday.
