A gunman clashed with police outside a Coptic church in Cairo on Friday after trying to break through security barriers protecting the site.
The order came just hours after gunmen attacked Mar Mina Church and a shop in southern Cairo, killing at least 10 people, including eight Christians, and wounding a number of others.
No one has claimed responsibility as of Friday morning, but the Islamic State has largely claimed responsibility for previous attacks on Christian churches in Egypt.
Officials said one gunman was shot dead shortly after the attack.
Egypt's beleaguered Christian minority make up around 10% of the population.
It was not clear if the three reported dead included the attacker, or how many attackers were involved. It also said there was a separate attack on a store in the same neighborhood of Helwan that killed two Copts.
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At least five people were wounded, Megahed said.
The ministry said security forces had "immediately dealt with the (attacker) and arrested him after he was wounded". The second attacker apparently fled, the agency reported. Dozens of people then rush out from hiding to tackle and beat the fallen gunman.
Ahead of the January 6 Christmas celebrations, Egypt's security apparatus has been on high alert, deploying security personnel at churches across the country.
After Friday's bloodshed, Egyptian President Abdel Fatah al-Sissi condemned the assault as "vicious".
A month later, ISIS gunmen shot dead about 30 Christians south of Cairo as they travelled to a monastery.