"The terrorist elements opened fire on the [security] forces who responded", the statement said.
The attack, the latest in a series of assaults targeting the country's Christian minority, was claimed by the Islamic State group, according to the group's Amaq news agency.
The Interior Ministry said the militants were killed in a shootout in the desert west of Minya province. He said he was praying for the "pilgrims killed for the sole fact of being Christians", asking that those grieving be comforted.
The ministry said the suspects were on the run from security forces when national security intelligence identified their location.
EI jihadists regularly attack Copts, who represent about 10% of the population of almost 100 million Nation.
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In May 2017, masked gunmen ordered Christians traveling to the Saint Samuel monastery to get off their buses and recant their faith.
In December 2017, a gunman killed 11 people at a church and a Christian-owned shop near Cairo.
Twin church bombings in April 2017 left more than 40 people dead, and in December a year ago a gunman killed nine people in a church in southern Cairo.
Egypt's President Abdel Fattah al-Sisi called for citizens to battle against religious discrimination.
Addressing a meeting of youths in the Red Sea resort city of Sharm el-Sheikh, el-Sissi on Sunday sought to send out a message of reconciliation.
They are the Middle East's largest Christian community and have long complained of persecution and insufficient protection.
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