The two groups clashed after Muslims attacked the Coptic Saint Mena Church in the working class neighbourhood of Imbaba to free a Christian woman they alleged was being held against her will because she wanted to convert to Islam.
A parish priest, Father Hermina, told AFP that at least five of the dead were Copts who died when "thugs and (Muslim fundamentalist) Salafis fired at them" in the late afternoon attack.
The Gospel had been laid on a body wrapped in a sheet that was lying inside the church. The church floor was bloodstained as wounded Christians were brought in for treatment.
Outside, military police parked several armoured cars to block off Muslim protesters.
They fired their guns into the air as Christians in front of the church and Muslim protesters down the street hurled stones at each other. The Muslim protesters threw firebombs, one of them setting an apartment near the church on fire.
"Oh God! Oh Jesus!" chanted the Coptic protesters. They scuffled with soldiers, blaming them for not doing enough to protect them.
The soldiers advanced at Muslim protesters who edged closer to the church, firing over their heads to repel them. Special forces were later deployed outside the church.
An officer ordered a soldier to escort an AFP journalist away from the church, saying "no journalists are allowed."
Hermina and witnesses had said the Muslims tried to storm the church earlier in the day, claiming the Christians were holding a Muslim woman.
Elsewhere in Imbaba, Muslim protesters threw firebombs at another church, setting it on fire, police officials said. They said the fire was put out.
At one of the cordons outside the St Mena church, Muslim protesters said they were first fired upon by the Copts, after they tried to find a Christian woman they say converted to Islam and was being held inside.
"They started firing on us. We were peaceful," said one of the protesters who gave his name as Mamduh. "We won't leave until they give up their weapons and the people who killed us are tried."
No weapons could be seen inside the church and the Copts there said they had none.
Egypt's mufti �" the government's chief interpreter of Islamic law �" Ali Gomaa condemned the clashes and said they "were toying with Egypt's national security."
The violence could not have been caused by "religious people who understand their religion, whether Muslim or Christian," he told the official MENA news agency.
The injured, who suffered from fractures and gunshot wounds, were taken to four city hospitals, medical officials said.
Copts account for up to 10 per cent of the country's 80 million people and they complain of discrimination, and have been the targets of fairly regular sectarian attacks.
Claims that Christian women who converted to Islam were kidnapped and held in churches or monasteries have soured relations between the two communities for months.
Egypt's military rulers had warned on May 1 of strong measures against anyone inciting sectarian strife, in a bid to ease tensions between Muslims and Christians.
The Supreme Council of the Armed Forces, which took power after president Hosni Mubarak's ouster in February, said it was "exerting all efforts to end sectarian disagreements on the Egyptian street to protect this nation."
The statement came after a series of Muslim-Christian clashes and amid the growing public presence of Salafis �" a puritanical Islamist sect �" since the fall of Mubarak after a wave of mass protests.
The Salafis have held protests outside the Coptic Church's headquarters in Cairo to demand the release of two women they alleged were being held after converting to Islam. The church denies the women converted to Islam.
The claim was picked up by an Al-Qaeda-linked group in Iraq that massacred dozens of Christians in a Baghdad church in November 2010 and vowed more attacks until the two women were freed.
Two months later, a suicide bomber killed more than 20 people outside a church after a New Year's Eve mass in Egypt's coastal city of Alexandria.
In the central province of Minya, security was boosted last month after a Christian-Muslim family dispute sparked deadly clashes, prompting Muslim residents to burn homes and shops owned by Coptic Christians.
The Minya incident came as thousands in the neighbouring province of Qena protested against the appointment of a Christian governor linked to the ousted Mubarak regime.