Pro- and anti-Morsi factions are organizing rallies in response to the president's move consolidating power even as he strengthens his hand abroad, having played a leading role in arranging a ceasefire between Israel and Hamas militants earlier this week.
Morsi appeared before his supporters outside the presidential palace, the BBC reported, where he told the crowds that he was "for all Egyptians."
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Muslim Brotherhood offices were set aflame in Port Said and Ismailia, the BBC said.
CNN reported protestors sacking the Muslim Brotherhood's headquarters in Alexandria.
In Cairo, the security forces responded by firing tear gas at protesters in Tahrir Square, witnesses told the Guardian.
Morsi's Thursday decree largely exempts him from judicial power and insulates the country's young leader from the demands of the constituent assembly, an influential body tasked with writing a new constitution, said AP.
The move sparked outcry among rights groups and the opposition, who denounced it as a grab for power.
Yet Morsi insisted today that he wanted to lead Egypt on the path to "freedom and democracy," according to the BBC, saying that he wanted to see a "genuine opposition, a strong opposition."
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The European Union has urged Egypt to respect the democratic process, Reuters reported, while a spokesman for United Nations Human Rights Commissioner Navi Pillay said the organization was "very concerned" about the impact on the rule of law and human rights.
Political heavyweight Mohamed El Baradei organized one of the anti-Morsi protests in Cairo today, said AP, while Morsi's Muslim Brotherhood party is holding a competing rally in front of the presidential palace.
Anti-Morsi protesters shouted slogans like, "the people want the regime down,” similar in tone to anti-Mubarak anger seen on the streets before his overthrow last year, said Bloomberg. They also held signs that said, "Morsi is the new Pharaoh," sentiment echoed by El Baradei in a Thursday tweet:
Morsi today usurped all state powers & appointed himself Egypt's new pharaoh. A major blow to the revolution that cld have dire consequences
— Mohamed ElBaradei (@ElBaradei) November 22, 2012
Anti-Morsi demonstrators demand the dissolution of cabinet and seek major reforms of the police force, according to Bloomberg.