Morsi, in a call to Coptic Pope Tawadros II, last night condemned the violence.
"I consider all attacks on the church as an attack on me personally," state television quoted Morsi as telling the pope.
One person has died and more than 60 others have been injured in clashes outside Cairo's Coptic cathedral following a funeral.
The memorial service at the cathedral, in the central Cairo neighborhood of Abbassiya, was being held for four Christians who were killed in sectarian clashes on Friday.
Mourners, who were chanting against President Morsi, were pelted with stones and bottles by residents of the area as they left the funeral.
The Copts inside the church complex hurled objects back at the rows of Abbassiya residents.