BBC reported that more than 50 police officers were killed during clashes, while local media said 35 citing security sources.
"A number of policemen" were killed in the operation, said the Egyptian interior ministry but did not reveal the exact casualty figures from the confrontation. At least 23 police officers were killed and the other victims were conscripts, the sources said.
Egyptian President Abdel-Fattah al-Sisi on Sunday urged security bodies to exert utmost efforts to hunt for the perpetrators of the Friday terrorist attack that left 16 policemen dead in the desert of Giza province. Those attacks were claimed by the Islamic State group.
The security forces are understood to have gone into the desert following a tip-off about a possible hideout.
The suspected fighters tried to flee after the exchange of fire there, the sources said, and continued to shoot at a second security unit called in for back-up from atop neighbouring buildings.
It also said that 13 policemen, including four officers and nine conscripts, were injured and one policeman was missing.
Britain prepares to face Storm Brian's 70mph winds
Storm Brian is expected to affect much of southern and western England and south and west Wales from early on Saturday morning. Storms in the United Kingdom and Ireland are named alphabetically and Brian will follow September's Storm Aileen.
No group immediately claimed involvement in Friday's attack.
The government accuses Hasm of being the militant arm of the outlawed Muslim Brotherhood but the organisation denied such accusations.
The armed group staging the campaign later pledged allegiance to ISIL in 2014.
The country has been under a state of emergency since bombings and suicide attacks targeting minority Coptic Christians killed scores earlier this year.
Terror attacks in Egypt used to be centered in North Sinai before spreading nationwide and killing hundreds of policemen and soldiers over the past few years.