The shootout broke out after members of the Egyptian National Police attacked the terrorist cell in Bahariya Oasis, a large area of 135 square kilometers, situated some 370 kilometers from the capital Cairo, on Friday, unnamed security sources said.
Egypt is battling armed groups concentrated in the Sinai peninsula, including an Islamic State of Iraq and the Levant (ISIL, also known as ISIS) affiliate, that has killed hundreds of security forces since 2013.
"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.
The statement said that the forces were looking for terrorists in the surrounding areas.
Hasm is a group that has claimed several attacks around Cairo targeting judges and policemen since previous year. Clashes erupted when they tried to arrest them and they exchanged fire.
At least 55 policemen were killed in the exchange of fire with the militants during a raid on a hideout near Cairo, Egypt.
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Interior Ministry said that a number of policemen were killed and injured, and some terrorists also died in the ensuing crossfire.
He too said eight other security personnel were wounded in the attack. The Muslim Brotherhood denies this.
A fake claim in the name of the small extremist group Hasm, reported by multiple local media, spread on social media soon after the attack.
Morsi was elected as Egypt's first civilian president in 2012, but the army overthrew him a year later following mass protests against his rule.
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.