The Anti-Coup Alliance said 10 marches would take off from various parts of the capital "to defend the electoral legitimacy" of Egypt's first freely elected president Morsi, ousted by the military on July 3.
His supporters, led by the Muslim Brotherhood, have kept up two huge protest camps in Cairo and said nothing short of his reinstatement will perusade them to disperse.
The call for fresh rallies comes as Al-Azhar, Sunni Islam's highest seat of learning, called for reconciliation talks in the latest of a string of attempts to find a peaceful solution to the political deadlock.
"Al-Azhar has been studying all the proposals for reconciliation put forward by political and intellectual figures... To come up with a compromise formula for all Egyptians," Tayyeb's advisor, Mahmud Azab, told the state-owned al-Ahram.
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Morsi's turbulent single year in power polarised Egyptians and his ouster by the military only deepened divisions.
The army-backed leadership is under immense pressure at home to crack down on the protests, and immense pressure from the international community to avoid bloodshed.
But the government vowed on Wednesday to clear the Islamist protest camps, saying foreign mediation had failed.
More than 250 people have been killed in clashes since Morsi's ouster by the military, following days of mass rallies demanding his resignation.
The government had already ordered police to end the pro-Morsi protests, which it described as a "national security threat.