Shenuda III was quoted by pan-Arab daily al-Quds al-Arabi as saying he wanted to "forcibly resist action of this kind."
He said he wanted to "work to restore calm and prevent further acts of violence in the city."
A group of Muslims reportedly gathered in the area of Giza where some 3,000 Coptic Christians were reported to have protested outside the office of the local governor.
The Muslims reportedly set several crucifixes alight and threw stones at the Copts.
Egypt's interior ministry said over 100 people were arrested over the violence in which one protester was killed and dozens of people were injured as police fired tear gas and the Copts threw stones and petrol bombs.
The Copts said they had permission to build the church in Giza but officials said they did not have the proper permit.
Protests on this scale are rare from Egypt's Christians, who make up about 10 percent of the country's 85 million population.
There has been friction in the past between the majority Muslims and Christians, who complain they do not have the same freedom to build places of worship.