Bishop Kyrillos William, administrator of the Coptic Catholic Patriarchate of Alexandria, and two other bishops condemned the document as an attack on human rights. The constitution was signed into law Dec. 26.
Speaking with Aid to the Church in Need, Bishop William said, "We were waiting for a constitution that represents the whole of Egypt but instead we have one that only represents one group of people.
"We can see that the religious orientation of this constitution prepares the way for an Islamic caliphate."
Bishops Joannes Zakaria of Luxor and Antonios Aziz Mina of Giza also told ACN that the constitution is a threat to civil liberties.
Bishop William said: "Everywhere in the constitution there are clauses saying everything should be in accordance with Islamic law.
"The president [Mohammed Morsi] promised to build a civic, modern and democratic state but we do not think that this constitution is in any way in accordance with that."
Among the bishops, there was concern that the constitution would force non-Muslim women to wear Islamic headscarves and would legitimize the marriage of under-age girls.
The bishops said that, apparently in line with Shari'a law, the constitution permits women who are "sexually mature" to marry, which they said strongly implies acceptance of teenage marriages.
Bishop Zakaria said: "The Islamists want to apply Shari'a law especially with regard to women. It is very bad for women and very bad for non-Muslims in society."
Principles and values
Saying that the constitution is "not good news" and "does not take into consideration human rights for all," Bishop Aziz added that the constitution implicitly sanctions child labour, only warning against forcing youngsters to do work that is too demanding for them.
Citing Article 219, Bishop William said: "The constitution not only outlines the principles of Shari'a but describes in detail all of the values and opinions contained in the Shari'a. It will be terrible -- everything will be interpreted according to Shari'a."
The bishops said that this heavy insistence on Shari'a undermined the credibility of Article 3 in the constitution which asserts the rights of Christians and Jews as well as Muslims.
Describing the constitution as the work of fundamentalist Muslims, Bishop Zakaria said: "It was already hard to get permission to repair a church in [former] President Mubarak's time, now it will be ever harder.
"But it will be much worse for Shiite Muslims, Baha'is, Buddhists and others who are not even recognized in the constitution."
The Coptic Orthodox Church withdrew in April 2012 from the talks on the constitution in protest at the reportedly Islamist content proposed. Coptic Catholic and Protestant representatives quickly followed suit. Secular parties also later pulled out.
The bishops said that the parliamentary elections due later this year will be a vote of confidence on the new constitution and the government's handling of it.
Bishop William said: "The people should fight for their rights. The Church cannot speak in their name but we can make people aware of the issues through our Justice and Peace committees."