The Grand Imam of Al-Azhar, Ahmed El-Tayyeb, met on Tuesday with senior figures from the Salafist Nour Party to discuss the party's propositions for national reconciliation.
The meeting included party head Younis Makhyoun and its vice-president Bassam El-Zarqa.
Egypt has seen mass demonstrations by supporters of Morsi since his ouster on 3 July by the military following nationwide protests demanding his resignation. The presidency has announced it aims to hold a process of national reconciliation and has called on the Brotherhood to take part.
The Muslim Brotherhood and its main Islamist ally Al-Gamaa Al-Islamiya have rejected the calls, insisting they will not take part in any talks or negotiations unless Morsi is reinstated.
The Nour Party, a former ally of the Brotherhood, supported the military-backed ouster of Morsi, as did Al-Azhar and the Coptic Orthodox Church.