Yohanna Naseef of St Mark's Catholic Orthodox Church in Alexandria said on Saturday that an annual meal attended by Christians and Muslims at his church had been cancelled after Friday's protests, in which three demonstrators died.
The Interior Ministery said 5000 people protested outside St George's Coptic Church in Alexandria on Friday over a play once performed there that they said was insulting to Islam.
Police used tear gas to disperse the crowd, which had pelted them with stones and re-grouped several times throughout the day.
Seven Christian-owned shops were attacked, Egypt's state news agency MENA reported.
It was the second protest in a week over the play and came two days after a young man stabbed a nun and a man at the church.
"The Christians have been at home since yesterday, they are afraid," Naseef told Reuters.
Subject of play
The play, called I Was Blind But Now I Can See, had been staged more than two years ago by youths, he said.
A recording of it had recently been posted on the internet by "extremists", Naseef said.
"Christians love their Muslim brothers"
Priest at St Mark's Catholic Orthodox Church
"The play was about extremism and against radicalism," he said.
It was based on a 1990s movie called The Terrorist, which starred Egyptian comedian Adel Imam.
The film dealt with the subject of militant Islamists, who were waging an uprising against the government at the time.
The protesters had been demanding an apology for the play. But Naseef said he saw no need to say sorry.
"Christianity rejects insulting any religions," he said. "Christians love their Muslim brothers."
St Mark's Church had cancelled its annual iftar meal on Saturday because of the protests, he said. Iftar is the Arabic name for breakfast eaten by Muslims at sundown during the Islamic fasting month of Ramadan.
The Grand Sheikh of al-Azhar mosque in Cairo, Mohammed Sayed Tantawi, and Coptic Pope Shenouda III issued a joint statement expressing sadness for the clashes.
They urged calm and called for resolving differences through dialogue.
Grand Sheikh Tantawi (above) and
Pope Shenouda III urged calm
Earlier on Saturday, Tantawi told MENA that people driven by personal interests were trying to "spread strife among the people of Egypt".
He did not elaborate on their motives.
"Their attempts will not succeed," he said.
Christians make up 10% of Egypt's mainly Muslim population of 72 million people.
Relations between the two communities are generally peaceful, but tensions sometimes flare.
In 1999, 22 people were killed in sectarian strife in the southern village of Kosheh, but such incidents are rare and are usually sparked by local disputes.