Some worshippers turn to alternative churches because of more lenient rules on separation.
At least 24 people have been killed and scores more injured in clashes between mostly Coptic demonstrators and military police outside the state television building in central Cairo.
Essam Sharaf, Egypt’s interim prime minister, called for a calm early on Monday morning as a curfew was imposed in central areas of the capital, including Tahrir Square.
Egypt’s leadership also held an emergency meeting late on Sunday to discuss the situation, with clashes also reported in Alexandria, Egypt’s second city. An emergency cabinet session is scheduled for Monday, a spokesman said.
The Copts say they were marching peacefully when thugs attacked them, drawing in the military police who used what activists described as unnecessary force.
The demonstrators, who were protesting the destruction of a church in southern Egypt, torched two armoured vehicles, six private cars and a public bus, security sources said. Scores of suspected assailants were arrested in the aftermath.
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From outside the television building the clashes spread to nearby Tahrir Square and the area around it, drawing in thousands of people.
They battled each other with stones and firebombs, some tearing up pavements and collecting stones in boxes for use as missiles. At one point, a group of youths with at least one riot policeman among them dragged a protester by his legs for a long distance.
An AFP news agency journalist also witnessed violence near a hospital in the city centre that had admitted people wounded in the clashes.
More than 200 people were injured, the health ministry said.
In an address aired on state television, Sharaf called for calm, describing the events as “unnecessary violence” and a “conspiracy”.
His cabinet said in a statement that it would “not let any group manipulate the issue of national unity in Egypt or delay the process of democratic transformation” which it said would begin with opening the doors to candidate nominations.
A committee of prominent figures from the Coptic church and Al-Azhar mosque are also due to meet on Monday, while presidential candidate Amr Moussa and political groups said they would hold an emergency meeting about the violence.
During the protest, led by several Coptic bishops, demonstrators burnt photos of Mustafa al-Sayed, the governor of Aswan province where the church was destroyed.
The church in Merinab village was attacked after al-Sayed was reported as saying Copts had built it without the required planning permission.
Al Jazeera’s Rawya Rageh, reporting from Cairo, said “utter chaos” prevailed in the centre of the capital.
Rageh said: “It was supposed to be a peaceful protest, demanding that Coptic rights should be fulfilled. But it soon escalated into violence, with people on balconies pelting the demonstrators with stones, clearly disagreeing with the cause of the Coptic demonstrators.”
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“The protest was peaceful. We wanted to hold a sit-in, as usual,” Essam Khalili, a protester wearing a white shirt with a cross drawn on it, said.
“Thugs attacked us and a military vehicle jumped over a sidewalk and ran over at least 10 people. I saw them.”
Wael Roufail, another protester, corroborated the account.
“I saw the vehicle running over the protesters. Then they opened fired at us,” he said.
Khalili said protesters set fire to army vehicles when they saw them hitting the protesters.
Television footage of the riots showed some of the Coptic protesters attacking a soldier, while a priest tried to protect him. One soldier collapsed in tears as ambulances rushed to the scene to take away the injured.
Copts blame Egypt’s ruling military council for being too lenient on those behind a spate of anti-Christian attacks since Hosni Mubarak was toppled from power in February.
About 10 per cent of the country’s more than 80 million people are Copts.
Tensions are not uncommon between Copts and the country’s Muslim majority. In March, 13 people were killed in sectarian clashes around the Cairo neighbourhood of Manshiyet Nasser after a church was torched in the village of Sol, south of the capital.