The police also deployed aircraft to confront the militants, the official said, speaking on condition of anonymity because he was not authorized to talk to reporters.
The interior ministry said a "number" of policemen had been killed as well as some militants, but did not elaborate. The ministry put the number of the casualties among the militants at 15.
Police on their way to a hideout used by the Hasm militant group reportedly came under attack with rocket-propelled grenades.
The militants, according to local media reports, belonged to the Hasm Movement, a relatively new group that Egypt's security forces claimed to be armed wing of the Muslim Brotherhood, the Islamist movement that once led the country and that is now outlawed.
The interior ministry said security forces hunting down militants in the region were attacked late Friday on a road to the Bahariya oasis, some 200 kilometers (125 miles) southwest of Cairo, AFP reported.
An official statement issued on October 21 said the incident would be investigated, suggesting that the heavy death toll may have been partially caused by incompetence, intelligence failures, or lack of coordination.
Hasm has claimed multiple attacks since 2016 on police, officials, and judges in Cairo.
Authorities are fighting the Egyptian branch of the Islamic State group, which has increased its attacks killing hundred of soldiers and police in the north of the Sinai peninsula, more than 500 kilometres away from the latest violence.
The statement said that the forces were looking for terrorists in the surrounding areas.
Terrorist attacks, mainly targeting police and military, increased after the ouster of former Islamist president Mohamed Morsi in 2013 by military following massive protests against his rule.
No militant group has yet claimed involvement in the Giza firefight.
Egypt has been under a state of emergency since earlier in the year when IS militants launched a series of bombings and suicide attacks that killed scores of Coptic Christians.