The Muslim Brotherhood Supreme Guide Mohamed Badie called on supporters he described as "the partners of the January revolution" to rally for "freedom and legality" on Friday.
Protesters should "reject the bloody military coup," Badie said, claiming "everyone has tasted its disasters."
Badie aimed his criticism at Defense Minister Abdel Fattah al-Sisi, who on Wednesday called for mass protests to mandate the army to confront "violence and terrorism."
The Muslim Brotherhood leader described the call as more catastrophic an act than demolishing the Kaaba at Mecca, the holiest site in the Muslim world.
In Badie's weekly speech addressed to Muslim Brotherhood members, posted on the the group’s website, he called on supporters not to resort to violence, even in the face of provocations from the other side.
On 3 July, Sisi had announced a roadmap for the future after mass protests involving millions of Egyptians demanded the overthrow of President Mohamed Morsy, who belongs to the Muslim Brotherhood.
Morsy supporters responded by staging a huge sit-in at Rabea al-Adaweya in eastern Cairo, now into its 29th day.
