Cairo investigation chief Mohamed el-Sharkawy said dozens of "gunmen and terrorists" were arrested in the confrontation, Ahram Online reported.
Nabil Farag, a Giza security assistant director, died of gunshot wounds during the raid, state TV reported.
Security troops raided Giza's Kerdasa district to arrest people accused of setting police stations on fire and of killing 11 security officers in clashes after the ouster of President Mohamed Morsi July 3.
The Interior Ministry said security personnel recovered dozens of weapons from the militants. After taking control of the area, police imposed a curfew.
"We will not back down until we've purged all pockets of terrorism [in Kerdasa]," Gen. Hani Abdel-Latif said.
The operation in Kerdasa followed Monday's crackdown in Dalja, partially controlled by Morsi supporters, Ahram Online said. Following Morsi's ouster, churches and police stations were attacked.
Security forces arrested 56 suspects Monday.
A curfew imposed in some areas will be shortened from midnight to 5 a.m. local time, except for Fridays when it will be from 7 p.m. until 5 a.m., Egypt's Cabinet announced Thursday. The curfew has been in place since mid-August in Cairo, Giza, Alexandria, Suez, Ismailia, Assiut, Sohag, Beni Suef, Minya, Beheira, South Sinai, North Sinai, Fayoum and Qena.
Last week, Interim President Adly Mansour issued a two-month extension of a state of emergency that was declared when security forces dispersed two pro-Morsi sit-ins Aug. 14.
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