The official says the coordinated attacks killed police guarding an administrative building, a TV station and a police station in El-Arish, the main city in northern Sinai near the border with Gaza and Israel.
The official spoke on condition of anonymity because he was not authorized to brief reporters.
Islamic militants, long active in the area, have intensified their attacks against security forces since the ouster of Islamist President Mohammed Morsi on July 3. The almost daily attacks have targeted the El-Arish airport, checkpoints and police stations.