It did not say when the gun battle took place, nor did it mention any casualties among security forces.
Islamic State claimed responsibility for Friday’s attack in Minya when gunmen targeted two buses near the Monastery of St. Samuel the Confessor, 260 km (160 miles) south of Cairo. The dead included six members of the same family.
Islamic State did not provide any evidence to back up its claim of responsibility, one of several in recent years as Egypt’s Christian minority has been repeatedly targeted.
The ministry said the suspects were on the run from security forces when national security intelligence identified their location.
“The area was raided and when it was surrounded the terrorist elements opened fire at the forces, which obliged them to deal with the source of the firing,” it said in the statement.
Security forces recovered weapons including automatic and semi-automatic rifles, shotguns and ammunition, the ministry said.
There had been a lull in major attacks since December, when a gunman attacked a church and a Christian-owned shop near Cairo.