Outside a mosque in the Mediterranean city of Alexandria, anti-Morsi crowds threw stones and firecrackers on Brotherhood backers who used prayer rugs to protect themselves, injuring at least 15. The protesters then stormed a nearby Brotherhood office.
State TV reported that offices of the Brotherhood's political arm were burned in the Suez Canal cities of Suez, Ismailia and Port Said, east of Cairo.
In the southern city of Assiut, ultraconservative Islamists and former jihadists outnumbered liberal and leftists in rival demonstrations. The two sides exchanged insults and scuffled briefly.
Morsi and the Brotherhood contend that supporters of the old regime are holding up progress toward democracy. They have focused on the judiciary, which many Egyptians see as too much under the sway of Mubarak-era judges and prosecutors and which has shaken up the political process several times with its rulings, including by dissolving the lower house of parliament, which the Brotherhood led.
His edicts effectively shut down the judiciary's ability to do so again. At the same time, the courts were the only civilian branch of government with a degree of independence: Morsi already holds not only executive power but also legislative authority, since there is no parliament.
His move came at a time when he was enjoying lavish praise from U.S. President Barack Obama and Secretary of State Hillary Rodham Clinton for brokering a cease-fire between Israel and Gaza's Hamas rulers on Wednesday. Clinton had been in Cairo for extensive talks with Morsi before the truce was announced.
U.S. State Department spokeswoman Victoria Nuland, said in a statement that the edicts raise "concerns" for many Egyptians and for the international community, adding that the country's revolution had aimed in part to prevent too much power from being concentrated in one person's hands.