Gunmen killed an Egyptian police captain and a conscript on a desert road outside Cairo on Sunday, the Interior Ministry said.
The ministry's media center said the joint security patrol was trying to stop a suspicious vehicle on the road to the canal city of Suez early in the morning when its occupants opened fire.
Captain Ashraf Badeer al-Qazaz was killed in the firefight, along with a conscript from the central security force. The assailants managed to flee.
On Saturday, a militant group called Ajnad Misr, or "Egypt's Soldiers," claimed responsibility for a bombing that killed a police officer late Friday in Cairo. The group said it is waging a campaign of retribution for the killing and detentions of protesters and young Egyptians.
In a video posted on militant websites last week, the group detailed eight of its operations since November last year that included firing on and hurling small bombs at policemen and checkpoints. It also claimed responsibility for three blasts earlier this month outside Cairo University that killed a police general and injured seven people.