Prime Minister Essam Sharaf chaired the meeting which opened with one minute of silence for those killed.
At least 40 people were arrested overnight after a protest by Copts in Cairo's Maspero district degenerated into deadly clashes which also left more than 200 people wounded, according to a security official.
The clashes rattled the Cairo stock exchange, which lost 5.15% within minutes of opening, reflecting fears for Egypt's political and economic future.
A curfew was imposed overnight in parts of the Egyptian capital following the clashes.
Copts had been holding a demonstration against an attack earlier this month on a church in the southern city of Aswan when the clashes broke out and there was fighting later near the hospital where casualties were taken.
In a late-night address, Sharaf appealed to Egyptians "not to give in to sedition" and warned that the country was "in danger."
The Sunni religious leader Ahmed Tayyeb called for crisis talks between Muslim and Christian leaders later on Monday "in a bid to contain the crisis." state television said.
Monday's newspapers ran bleak headlines, with the independent daily Al-Masry al-Youm lamenting "A black night for Egypt's revolution."
Fuad Allam, who headed Egypt's security services for two decades told Al-Arabiya satellite television that discriminatory religious laws had to be amended.
But others said the clashes were not only fuelled by sectarian strife but also anger towards the security services and the ruling military council which succeeded Mubarak in February.
As military police gave assurances that calm had returned to the capital, Sharaf warned on public television that Egypt was "in danger"
Sharaf, appointed by the military council which took power after mass
protests led to Mubarak's fall, heads a caretaker government in the runup to