Prime Minister Essam Sharaf called a crisis cabinet meeting after the violence which left 186 injured and a church on fire.
The clashes took place in the working-class neighbourhood of Imbaba, in north-west
Cairo, after Muslims attacked the Coptic Saint Mena church to free a Christian woman they alleged was being held against her will because she wanted to convert to Islam.
Estimates of how many Christians and how many Muslims had died varied on Sunday morning.
Elsewhere in Imbaba, Muslim protesters threw firebombs at another church, setting it on fire, police officials said. They said the fire was put out.
Sharaf cancelled a trip to Bahrain and the United Arab Emirates and called an emergency meeting of the government because of what a spokesperson termed “the regrettable events in Imbaba”.
The area was sealed off and security stepped up around key churches in the country, senior security official Mohsen Murad told state TV.
The government's chief interpreter of Islamic law, Mufti Ali Gomaa, condemned the clashes and said the attackers "were toying with Egypt’s national security".
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.