"We call for a million person march under the banner of 'Martyrs of the Coup' on Tuesday," the Anti-Coup Alliance of Islamist groups organising the protests said in a statement.
Also today, pro-Morsi Wasat Party head Abul Ela Mady and his deputy Essam Sultan were both arrested in Cairo for involvement in killing protesters in recent violence.
In the worst violence seen since 61-year-old Morsi was deposed by the army on July 3, 80 people were killed in clashes with the security forces on Saturday.
Both men were arrested on charges of inciting violence, killing protesters and insulting Egypt's judiciary.
Mady and Sultan were arrested in the Moqattam district of the Egyptian capital, and were then sent to Aqrab prison, where nine Muslim Brotherhood leaders are being held, state-run MENA news agency reported.
Prosecutors also ordered the arrest of Safwat Hegazy, a preacher known for his ties with the Muslim Brotherhood, on charges of inciting violence, after he led a march from Rabea al-Adaweya sit-in to Nasr Road which degenerated into deadly clashes with security forces.
Muslim Brotherhood spokesman Gehad el-Haddaf was quoted by the BBC as saying that there was no intervention by the military and no confrontation.
He said the march "circled the building for a good 10 to 15 minutes with a lot of chants of 'down with the coup'". However, one report suggests many turned back before reaching the building.
Protesters are continuing to stage large sit-ins in the capital to call for Morsi's reinstatement.
Meanwhile, EU foreign policy chief Catherine Ashton is in Cairo for talks. She will meet leaders of Morsi's Muslim Brotherhood, head of the Egyptian armed forces Gen Fattah al-Sisi and interim President Adly Mansour.
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