Flag-waving demonstrators are chanting slogans accusing the president and the Muslim Brotherhood of betraying last year’s revolution.
On Monday Mohamed Morsi sought to defuse the crisis by saying the decree granting him new powers was limited in scope.
However, his opponents want him to withdraw the measure completely.
Ahead of Tuesday’s rally, opposition activists clashed with police. A protester, who was in his fifties, died of a heart attack after inhaling tear gas.
Activists later converged on Tahrir Square – the main focus of the revolution that ousted President Hosni Mubarak – for one of the largest demonstrations to date against Mohamed Morsi.
“The people want to bring down the regime,” marchers chanted, echoing slogans used in last year’s protests.
“We don’t want a dictatorship again. The Mubarak regime was a dictatorship. We had a revolution to have justice and freedom,” protester Ahmed Husseini was quoted as saying by Reuters news agency.
Journalists, lawyers as well as opposition figures including Nobel Peace Prize laureate Mohammed ElBaradei were expected to join Tuesday’s rally.
Protests are also being held in Alexandria and other cities.
The president’s decree, known as the constitutional declaration, said no authority could revoke his decisions.
There is a bar on judges dissolving the assembly drawing up a new constitution. The president is also authorized to take any measures to preserve the revolution, national unity or safeguard national security.
Critics say the decree is an attack on the judiciary. It has sparked violent protests across the country.
On Monday Mohamed Morsi told senior judges that the scope of the measure would be restricted to “sovereign matters”, designed to protect institutions.
The Muslim Brotherhood, which supports President Mohamed Morsi, said it was postponing its own demonstration, originally due on Tuesday, to avoid “public tension”.
The postponement is another sign that the government wants to defuse confrontation, but it remains to be seen whether it ends the days of angry and sometimes violent protests.
Egypt’s union of judges, known as the Judges Club, rejected the president’s statement, calling it “worthless” and said they would continue to suspend work in courts.
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