"Prime Minister Sharaf has called for an emergency meeting of the cabinet to discuss the regrettable events in Imbaba," Ahmed al-Saman, a cabinet spokesman told the official MENA news agency.
Sharaf "has decided to postpone his visit to Bahrain and the United Arab Emirates" which had been scheduled for Sunday, state TV reported.
Clashes between Muslims and Christians in the Cairo working class neighbourhood of Imbaba on Saturday left nine dead and more than 100 injured.
State TV said that six Muslims and three Copts had been killed. A parish priest, Father Hermina, had told AFP on Saturday that at least five of the dead were Copts.
The area in Imbaba has been sealed off and security has been stepped out around key churches in the country, senior security official Mohsen Murad told state TV.
The two camps had clashed on Saturday 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.
Elsewhere in Imbaba, Muslim protesters threw firebombs at another church, setting it on fire, police officials said. They said the fire was put out.
Copts account for up to 10 percent 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.