The three were in a mass of people paying respects Monday to Pope Shenouda III, who died Saturday at age 88 after a long illness.
Tens of thousands of people assembled outside the church, waiting for a chance to view the body, officials said.
Authorities appealed to mourners to avoid overcrowding, telling them they would have time to view the pope's body, which is to remain in state until his funeral Tuesday, Sky News reported.
"It's a great loss for Egypt. He was wise and was widely listened to. He will be missed at a time when we need wisdom and a patriotic spirit," Tourism Minister Munir Fakhry Abdelnur said.
Shenouda's death set in motion the process to elect a new patriarch for the Christian Coptic community, which numbers about 18 million worldwide.
Bishops from around the world were traveling to Cairo to attend the funeral, the British network said.
Shenouda is to be buried at the St. Bishoy Monastery in Wadi al-Natroun in accordance with wishes stated in his will, Ahram Online said.
Shenouda was elected pope of the Coptic Orthodox Church of Alexandria in 1971 but was stripped of his papacy and placed under virtual house arrest at a desert monastery in 1981 by Egyptian President Anwar Sadat in a dispute over Sadat's handling of the issues of Israel and rising Islamism. Sadat was assassinated later that year and Shenouda's papal position was fully restored in 1985 by Sadat's successor, Hosni Mubarak.