The head of Egypt's leading Islamic authority Al-Azhar, Sheikh Ahmed al-Tayeb, has begun calling on political powers and public figures to attend a national reconciliation meeting later this week.
The exact date of the forum, spearheaded by the Grand Sheikh of Al-Azhar, has not been announced yet.
According to the state-owned Al-Ahram newspaper, on Sunday, Al-Azhar would call the figures it wants at the meeting to "discuss them in preparation for the national reconciliation meeting."
In response, the Muslim Brotherhood has said it will not accept unconstitutional and illegitimate initiatives, meaning that deposed President Mohamed Morsi should be reinstated before its members engage in talks.
Ahmed Aref, spokesman for the Freedom and Justice Party (FJP), said that the Muslim Brotherhood sees al-Tayeb, who it says supported a "coup", as a separate entity from the Al-Azhar institution, according to state media.
The FJP is the political arm of the Muslim Brotherhood.
Al Jazeera's Rawya Rageh, reporting from Cairo, said: "It's going to be a difficult position for Al-Azhar when inviting the Muslim Brotherhood, given that the Grand Sheikh had openly backed the military in its campaign to remove Morsi from office."
Discussions about the proposed meeting come as thousands of Morsi supporters continue their protest in Cairo, despite warnings of a military crackdown.
On Sunday, the pro-Morsi Anti Coup alliance group announced that marches in Cairo would begin in the late afternoon from 10 locations and gather at the ongoing sit-ins at the Rabaa al-Adaweya and Nahda squares.
Ban Ki-moon, UN secretary-general, said he was deeply concerned about the crisis and called on all sides to urgently reconsider their actions and language.
Morsi was removed from office last month by the military, following weeks of anti-government protests.
The Anti-Coup Alliance wrote in a recent statement that "the days will only increase their determination to persist in their peaceful struggle until the country returns to the democratic path, until the coup is completely ended."
At least 28 pro-Morsi protesters and one police officer were injured when clashes broke out between demonstrators and police on Friday outside the security directorate in Fayoum.
Nearly 300 people have been killed in political violence since the overthrow.