The call comes after a disappointing turnout on Islamist protests last Friday, with observers suggesting that a deadly security clampdown on the Brotherhood have hampered the movement's mobilizing abilities.
The National Alliance in Support of Legitimacy said the people would rise up to reclaim the revolution "which the coup leaders have tried to steal... for the benefit of the Mubarak regime and the U.S.-Zionist alliance," referring to the United States and Israel.
Hundreds of Morsi supporters were killed on August 14 when police cleared out two sit-ins where they had been camped out since before his ouster, which the Islamists say was a military coup aimed at restoring the Mubarak regime.
Liberal and leftist forces, who are serving in an interim government, say that Morsi ruled in an authoritarian manner and was ineffective in addressing a faltering economy.
Meanwhile on Thursday, Egyptian police captured senior Muslim Brotherhood official Mohamed El-Beltagi, security sources said, as they pressed on with a crackdown that has put many of the Islamist group's leaders behind bars in recent weeks.
Beltagi appeared in a recorded statement aired by the Qatari-owned Al Jazeera television news network late on Thursday in which he urged Egyptians to join rallies against the military on Friday.
The crackdown on the group began after Egypt's army deposed President Mohammed Morsi, a Muslim Brotherhood member, on July 3.
Want to enjoy 'Zen' reading - with no ads and just the article? Subscribe todaySubscribe now