Masked attackers shot three policemen guarding a police station in the North Sinai town of El-Arish before fleeing, a security official said.
Later, unidentified assailants in a car fired at an armoured military vehicle in the south of the town, killing a soldier before fleeing, said the same source.
In the Sheikh Zuwayed area, near the border with the Gaza Strip, gunmen opened fire near a checkpoint, killing a civilian, another official said.
Dozens of soldiers and policemen have been killed in daily attacks, as the army has poured troops and armour into the lawless peninsula that straddles Africa and Asia to crush the insurgency.
The Sinai offensive comes as part of a massive crackdown by the army-installed authorities on Islamists, which has seen hundreds killed and more than 2,000 arrested nationwide.
Morsi, the country's first democratically elected leader, is himself detained, as is the leadership of his Muslim Brotherhood.