In a message relayed by the Italian episcopal news agency SIR, Catholic Coptic Patriarch Ibrahim Isaac Sidrak said there were no real divisions between Christians and Muslims in Egypt.
He also thanked the military and the police in Egypt "for all their efforts in protecting the country".
The patriarch said he "categorically rejected any internal inference in Egypt's internal affairs".
"We thank all those of our fellow Muslim citizens who have shown themselves to be so close to us and have tried to defend our churches and institutions," he said.
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"This is not a political conflict between different factions but a struggle by all Egyptians against terrorism," the patriarch said.
Monsignor Yohanna Golta, auxiliary Catholic bishop in Alexandria, said that "Christians and Muslims in Egypt are being persecuted by the Muslim Brotherhood".
"This is not a Christian-Muslim problem since it is an Egyptian problem. Everything happening is against the Egyptian people," Golta said on Vatican radio.
Egypt's Christian minority has overwhelmingly supported Morsi's overthrow. There are around 250,000 Coptic Catholics in Egypt and some seven million Coptic Orthodox believers.