The military published the statement on its spokesman´s Facebook page as scores were injured in clashes between the Islamist Morsi´s supporters and opponents in the Nile Delta ahead of the planned rallies.[break]
In the restive Sinai peninsula, a soldier was killed in an attack by Islamist militants early Friday, as gunmen ambushed several army and police positions with machine gun fire and rockets.
Some militants in the peninsula had threatened a violent response after Morsi´s ouster on Wednesday.
The military statement said it supported the right to peaceful protest, but warned that violence and civil disobedience acts such as blocking roads would "harm social peace."
The clashes in the Nile Delta province of Sharqiya broke out hours after chief justice Adly Mansour, 67, was sworn in as interim president until new elections, at a ceremony broadcast live from the Supreme Constitutional Court.
The Islamists accuse the military of conducting a brazen coup against Morsi, Egypt´s first democratically elected but controversial president, following massive protests calling for the Islamist´s ouster.
Morsi´s Musim Brotherhood movement has called for peaceful protests on Friday against the "coup," as police continue to hunt its leaders.
The military statement said "exceptional and autocratic measures against any political group" should be avoided, even as security forces rounded up top Muslim Brotherhood officials.
Police arrested the Brotherhood´s supreme leader Mohammed Badie "for inciting the killing of protesters", a security official told AFP.
Former supreme guide Mahdi Akef was also arrested, state television reported.
Morsi himself was "preventively detained" by the military, a senior officer had told AFP early Thursday, hours after his overthrow the night before, suggesting the ousted president might face trial.
"The armed forces believe that the forgiving nature and manners of the Egyptian people, and the eternal values of Islam, do not allow us to turn to revenge and gloating," the army said in its statement.
The United States on Thursday pressed Egyptian officials to avoid the "arbitrary arrests" of ousted Islamist president Mohamed Morsi and his supporters, a US administration official said.
Morsi´s government unravelled late on Wednesday after the army gave him a 48-hour ultimatum in the wake of massive demonstrations since June 30 against his turbulent year in office.
In Cairo, anger gave way to gloom as thousands of the embattled Islamist movement´s supporters rallied at a mosque, surrounded by the army.
"It´s a soft military coup. The military was smart, using the cover of civilians," said one, 26-year-old Ahmed al-Sayyed, in reference to the mass anti-Morsi protests.
Military chief General Abdel Fattah al-Sisi announced Morsi´s overthrow on Wednesday night, citing his inability to end a deepening political crisis, as dozens of armoured personnel carriers streamed onto Cairo´s streets.
A judicial source said the prosecution would on Monday begin questioning Brotherhood members, including Morsi, for "insulting the judiciary".
Other leaders of the movement would be questioned on the same charges, including the head of its political arm Saad al-Katatni, Mohammed al-Beltagui, Gamal Gibril and Taher Abdel Mohsen.
Morsi and 35 other Brotherhood leaders have also had a travel ban imposed on them.
Analysts said Morsi and his Islamists hastened their own demise.
"Morsi and the Brotherhood made almost every conceivable mistake... they alienated potential allies, ignored rising discontent, (and) focused more on consolidating their rule than on using what tools they did have," Nathan Brown wrote on the New Republic website.
Morsi´s supporters argue the president was confronted at every turn with a hostile bureaucracy left over by former strongman Hosni Mubarak, overthrown in an early 2011 uprising.
Morsi had issued a defiant call for supporters to protect his elected "legitimacy", in a recorded speech hours after the military announced his ouster.
"We had to confront it at some point, this threatening rhetoric," a senior military officer told AFP. "He succeeded in creating enmity between Egyptians."
Morsi´s rule was marked by a spiralling economic crisis, shortages of fuel and often deadly opposition protests.
Thousands of protesters dispersed after celebrating wildly through the night at the news of his downfall.
Egypt´s press almost unanimously hailed Morsi´s ouster as a "legitimate" revolution.
"And the people´s revolution was victorious," read the front page of state-owned Al-Akhbar.
US President Barack Obama said he was "deeply concerned" over Morsi´s ouster and urged the army to refrain from "arbitrary arrests".
In May, Washington approved $1.3 billion in military aid to Egypt. That was now under review, said Obama, as he called for a swift return to democratic rule.
Germany called the military´s move "a major setback for democracy in Egypt", while UN chief Ban Ki-moon said civilian rule should resume as soon as possible.
Governments across the Middle East welcomed Morsi´s ouster in varying degrees, with war-hit Syria calling it a "great achievement".
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