His party's offices were torched, while his opponents called the president a "dictator" and "pharaoh" who has now acquired more political might than ousted leader Hosni Mubarak.
There was fierce fighting in Alexandria following afternoon prayers, as thousands of opposing protesters hurled rocks and broken masonry at each other outside a mosque.
State television reported that mobs in a number of cities had set fire to the offices of the Freedom and Justice Party, the political wing of Mr Morsi's Muslim Brotherhood.
The group's headquarters in Suez, Port Said and Ismailia were all said to have been targets.
Youths had been involved in clashes with police in Mohamed Mahmoud Street – scene of deadly riots a year ago – since Monday. But as enormous crowds filed into Tahrir Square, the violence appeared to be escalating.
Mohamed ElBaradei, the one-time presidential candidate who had previously negotiated a political truce with Mr Morsi, claimed that the president had appointed himself the "new pharaoh" following the constitutional declaration he issued.
"Morsi today usurped all state powers," he wrote on Twitter shortly after the Egyptian leader's surprise statement, in which he confirmed that he had granted himself legislative and constitutional powers.
Mr ElBaradei added that the move was a "major blow" which could have "dire consequences".
Worrying political battle lines were developing in Cairo as huge groups of rival protesters staged separate rallies.
Outside the Presidential Palace, thousands of Muslim Brotherhood members arrived to celebrate Mr Morsi's announcement – a move which grants him immunity from judicial oversight along with vague new powers to protect the "goals of the revolution".
Giving a speech to his supporters, Mr Morsi said the declaration had been made to safeguard the future of the nation. "We are, God willing, moving forward, and no one stands in our way," he said.
"Victory does not come without a clear plan and this is what I have."
In his decree, Mr Morsi also vowed to re-examine criminal cases against officials accused of killing protesters during the Egyptian uprising – an apparent sop to activists who remain outraged that so few police officers have been brought to justice over the past two years.
Yet as bewilderment turned to anger, several thousand protesters marched on Tahrir Square in scenes reminiscent of the January 2011 protests that eventually toppled President Mubarak.
Brotherhood officials have argued that Mr Morsi's decree was necessary to ensure Egypt's revolution does not grind to a halt as a result of fractious political infighting and sabotage by elements from the old regime.
Yet critics say that Mr Morsi's arbitrary declaration may prove dangerously counter-productive.
"He now has more power than Hosni Mubarak," said Koert Debeuf, a representative of the EU Parliament based in Cairo. "The way to democracy cannot pass through dictatorship. There has been a danger of political chaos in Egypt. So in a certain way, maybe he was trying to avoid that by issuing the declaration. But by doing so he has created even more chaos." (© Independent News Service)