Egypt's state news agency MENA says security forces have killed 12 armed militants in the country's western desert.
No police were killed in the incident Friday.
MENA reported that an anonymous security source said, "Security forces dealt a severe blow to the terrorist elements in revenge for the blood of the men who were martyred last week..."
The shootout happened about 175 kilometers southwest of Cairo, near the location of last week's deadly attack on police.
Authorities say at least 30 Egyptian policemen were kill ed last week in a western desert shootout with militants, about 135 kilometers southwest of Cairo.
Security officials say the policemen came under fire as they were searching for suspected members of Hasm, a group that has claimed responsibility for several attacks in Egypt during the past year.
An Islamist insurgency has grown in Egypt since the military overthrew President Mohamed Morsi of the Muslim Brotherhood in 2013.
The insurgency, which includes the Egyptian branch of the Islamic State, has been concentrated in the northern Sinai Peninsula, but attacks have spread in the mainland, including in the capital where suicide bombers have struck churches and security headquarters.
Egypt has been under a state of emergency since April after suicide bombers struck two churches north of Cairo, killing scores of Christians.