Christians, who make up 10 to 15 per cent of Egypt's 85 million population, need special presidential permits in order to build or renovate churches in Egypt.
Supporters of equal rights for all citizens have long demanded the freedom to build and renovate churches without restraint in order to ensure parity between Egypt's religions.
The 50-member committee had initially adopted an article which stipulates "absolute freedom of belief" for Egyptian citizens and endows the state with the responsibility to ensure free practice of religion.
Sources at the meeting told al Ahram newspaper that representatives of the church, who have until now strongly supported complete freedom of religion, sided with Al-Azhar's objection.
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Articles regarding religion have been especially contentious during the committee's drafting session.
Article 47, allowing for complete freedom of religion, is controversial because it could be extended to other Egyptian minorities, such as Egypt's Bahais and Shia Muslims.
The Islamist-drafted 2012 constitution, which is currently being amended, did not grant equal rights to Christians and failed to recognise non-Sunni Muslims.