Two people were killed in clashes outside Cairo's main cathedral on Sunday, Egyptian officials now say.
Calm returned to central Abbassiya area where police deployed heavily outside St Mark's Cathedral. Several Coptic demonstrators were still gathered there on Monday morning.
Sunday's violence followed the funerals of four Coptic Christians killed in religious violence on Saturday.
Mourners leaving St Mark's Cathedral clashed with local residents.
Police fired tear gas to break up the violence. More than 89 people were injured, the state news agency said.
The health ministry said one Christian man was killed in Sunday's clashes. The other victim of the violence has not been identified.
Mourners inside the church had earlier chanted slogans against Egypt's Islamist President, Mohammed Morsi.
Witnesses told local TV stations that the violence started when a mob attacked mourners as they left the cathedral, pelting them with stones and petrol bombs. There was initially little police presence.
The Christians responded by throwing stones back, the witnesses said, until police arrived and attempted to quell the unrest, firing tear gas into the cathedral compound.
Appeals for calm
Mr Morsi denounced the violence in a phone call to Pope Tawadros II, the head of the Coptic Christian Church.
"Any attack against the cathedral is like an attack against me personally," he was reported as saying. He also called for an immediate investigation.
Pope Tawadros, who took office in November, appealed for calm.
The political arm of the Muslim Brotherhood, the Freedom and Justice Party (FJP), posted a statement on its Facebook page stressing its "utter rejection and condemnation of violence".
It urged both sides "not to respond to systematic provocations" or "ploys that target the homeland", but did not say who might be responsible for inciting the violence.
Egypt's minority of Coptic Christians, who make up about 10% of the population, have accused the government of failing to protect them, following the fall of Hosni Mubarak in 2011.
Clashes between Muslims and Coptic Christians have been seen numerous times since then, but this weekend's violence was the worst seen in several months.
Police said five deaths - four Copts and one Muslim - occurred on Saturday in Khosous, about 10 miles (15km) north of Cairo, after inflammatory symbols were drawn on an Islamic institute, provoking an argument.
The dispute escalated into a gun battle between Christian and Muslim residents, while Christian-owned shops were also attacked.
Violence there flared again on Sunday, with police reporting more sectarian fighting on the streets and clashes between police and youths.