"I call on Egyptian officers and soldiers to refuse orders to kill demonstrators," al-Qaradawi said in an address to the Egyptian people aired on Al Jazeera's live Egypt channel on Thursday.
Army chief and Defense Minister Abdel-Fattah al-Sisi on Wednesday urged Egyptians to take to the streets for mass protests on Friday to "authorize" him to "confront violence and terrorism."
"I'm asking the Egyptian people to go out like they did on June 30 and July 3," he said in a televised address. "I want you to show the world that you are authorizing me to confront any possible violence and terrorism."
Al-Qaradawi questioned al-Sisi's intention to turn Egyptians against one another.
"Why are we describing peaceful protesters as terrorists?" he asked.
"The Egyptian people have rejected the ouster of the elected president and the suspension of the constitution," he added.
The army overthrew Morsi on July 3 following mass protests against his regime.
It also suspended the constitution and installed Adly Mansour, the head of Egypt's constitutional court, as interim president in line with an army-imposed roadmap for the upcoming transitional phase.
Defiant Morsi supporters, for their part, have since been staging daily demonstrations and sit-ins nationwide to defend his democratic legitimacy and demand his reinstatement.
They, too, are currently preparing for mass Friday protests as part of an ongoing campaign against what they view as a "military coup against constitutional legitimacy."
The army said Thursday that al-Sisi's call was not directed at any particular political party or group.
"There was no threat to particular political parties. This is a national initiative to confront violence and terrorism, which threatens the Egyptian people's revolution and security," an army spokesman declared via Facebook on Thursday.
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