Egypt's military has warned against revenge attacks, after it toppled president Mohamed Morsi.
The call came as police began rounding up senior Islamists ahead of planned rallies by Morsi's supporters today.
A military statement says it supports the right to peaceful protest, but warned that violence and civil disobedience acts such as blocking roads will "harm social peace."
Clashes broke out in a number of districts of the capital Cairo hours after chief justice Adly Mansour, was sworn in as interim president.
In the restive Sinai peninsula, a soldier was killed in an attack by Islamist militants early this morning, 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 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".
Morsi himself was "preventively detained" by the military, 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.
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.