Supporters of ousted Egyptian President Mohammed Morsi called for mass demonstrations on Friday to show opposition to "the heinous coup against popular will."
A statement on the Muslim Brotherhood's website said that peaceful protest was "a right guaranteed to all Egyptians," saying it would hold the government responsible for its supporters' security.
The protests were given various names, including the "Friday of Rage" and the "Friday of Rejection."
Dozens of people have been killed in clashes between rival factions, police and soldiers since last weekend, with millions of people taking part in anti-Morsi protests.
Morsi was ousted as president by the military on Wednesday and replaced by top judge Adly Mansour on Thursday. Fresh elections have been promised.
The statement on the Brotherhood's website appealed to "the masses of the Egyptian people to mobilize in peaceful mass marches in all liberty squares and streets of Egypt, to be started from all mosques, after Friday prayers, to reject the heinous coup against popular will."
It was attributed to the "National Alliance in Support of Electoral Legitimacy."
"NASEL said that it feels rising public anger and the imminent danger threatening the nation as a result of the unprecedented military coup d'état against legitimacy derived from the will of the people," it said.
Morsi is under house arrest and the statement said NASEL would hold the "coup masterminds" responsible for his safety and "for preventing the elected president from contact with the people."
The Brotherhood denounced the crackdown, including the shutdown Wednesday night of its television channel, Misr25, its newspaper and three pro-Morsi Islamist TV stations. The military, it said, is returning Egypt to the practices of "the dark, repressive, dictatorial and corrupt ages."
On Thursday, a judge said that an investigation was being held into accusations that Morsi and eight other senior Muslim Brotherhood figures had defamed the judiciary. The arrests of Mohammed Badie, the Muslim Brotherhood's supreme guide, and a top deputy, Khairat el-Shater, were also ordered.
Authorities have issued a wanted list for more than 200 Brotherhood members and leaders of other Islamist groups.
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Military spokesman Col. Ahmed Mohammed Ali said in a Facebook posting that that the army and security forces will not take "any exceptional or arbitrary measures" against any political group, The Associated Press reported.
The military has a "strong will to ensure national reconciliation, constructive justice and tolerance," he wrote.
He spoke against "gloating" and vengeance, saying only peaceful protests will be tolerated and urging Egyptians not to attack Brotherhood offices to avert an "endless cycle of revenge."
The National Salvation Front, the top opposition political group during Morsi's presidency, called for all sides – "particularly political Islamic groups" -- to be included in the new political process, the AP reported.
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"Reconciliation is the name of the game, including the Muslim Brotherhood. We need to be inclusive," Munir Fakhry Abdel-Nour, a leading member of the group, told the news service. "The detentions are a mistake."
Egypt's newly appointed Foreign Minister Mohamed Kamel Amr said that Secretary of State John Kerry had expressed concern during a telephone call on Thursday for human rights, Reuters reported.
"He was worried about the status of human rights," Amr said, adding this was understandable. "I assured him there is no retribution, no acts of vengeance, that nobody will be treated outside the law."
Amr, a career diplomat who tended his resignation to Morsi after Sunday's anti-government protests, said he had spent the day calling international counterparts and briefing ambassadors with the message that there had been no "military coup" in Egypt. The army had merely heeded the popular will.
Of his conversation with Kerry, he said: "I told him that the main aim of the military now is to maintain security."
"There will be no acts of violence, no acts of exclusion. Everybody will be included. The idea is to have everybody participating in the transitional process."
Reuters and The Associated Press contributed to this report.