The three militant deaths come after a gunman shot dead nine people, including six Coptic Christians and a policeman. Police said the suspected attacker, Ibrahim Ismail, had been involved in previous deadly attacks.
Egypt's Interior Ministry said three militants were killed in a shootout with Egyptian police near Cairo on Saturday, one day after a gunman killed nine people in attacks on a Coptic church and a nearby store.
The militants were killed during a police raid on a farm used as a hideout in Giza, south of Cairo. They were allegedly linked to Hasm, an extremist group that Egyptian authorities say is the armed wing of the now outlawed Muslim Brotherhood.
Read more: Gunmen launch deadly attack on Coptic church
Six Coptic Christians and a policeman were killed on Friday when a gunman on a motorcycle opened fire at security guards outside the Mar Mina Church in Cairo's southern district of Helwan.
Earlier Friday, the same suspect had shot at a store owned by a Copt in Helwan, killing two people inside, according to the Interior Ministry.
'Islamic State' claims responsibility
The ministry, which is in charge of police, also said 10 other suspects linked to Hasm had been arrested in security crackdowns in the city of Qalubiya, north of Cairo, and the province of Fayoum in southern Egypt.
Read more: Crowds attack Coptic church in Egypt
The group had planned to carry out attacks against key institutions and security forces "in order to foment instability," the ministry said in an online statement.
The suspected assailant was injured in an exchange of fire with police outside the church and was arrested. He was identified as Ibrahim Ismail, 33, who police said had been involved in previous deadly attacks.
The "Islamic State" (IS) extremist militia has claimed responsibility for Friday's shootings.
Coptic Christians make up 10 percent of Egypt's population of 93 million people. The attacks have prompted Egyptian authorities to tighten security around churches ahead of Coptic Christmas on January 7.
law/cmk (AP, dpa)