Abdel Fattah al-Sisi said he was not calling for public unrest and wanted national reconciliation.
The army removed President Mohammed Morsi from power on 3 July, triggering huge street protests by his supporters.
The Muslim Brotherhood and other supporters of Mr Morsi say they will go ahead with their own rallies on Friday, despite General Sisi's statement.
Senior Brotherhood figure Mohamed el-Beltagy said Gen Sisi was "calling for a civil war... to protect this military coup".
In a speech at a military graduation ceremony, which was broadcast on television, Gen Sisi said: "I urge the people to take to the streets this coming Friday to prove their will and give me, the army and police, a mandate to confront possible violence and terrorism."
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