The attack took place near Badrasheen, a town some 20 kilometres from Cairo, where militants have also targeted police in the past.
The killings came as police and the army said they are closing in on militants and jihadists following a spate of attacks in the Nile Valley and the Sinai Peninsula.
Egypt has struggled to quell the Islamic State jihadist group based in the Sinai Peninsula and smaller militant groups in the mainland since the military overthrew Islamist president Mohamed Morsi in 2013 and cracked down on his supporters.
The interior ministry said a day later that it had killed 14 alleged IS members in a raid on a training camp in the eastern province of Ismailiya.
Earlier this week, the ministry said police had killed six IS militants in a shootout in southern Egypt.
While smaller groups like Hasam have mostly targeted policemen and government officials, IS has also attacked foreign tourists and Egypt's Coptic Christian minority.
Yesterday, Christian churches said they were suspending some activities such as conferences and religious trips for three weeks over security concerns.
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