Shouts of "Erhal! Erhal!" — Arabic for "Leave! Leave!" — and "The people want to topple the regime!" rose up from the crowd, the same chants used against Mubarak. This time, though, they were directed at his successor, Egypt's first democratically elected president.
"The same way we brought down Mubarak in 18 days, we can bring down Morsi in less," Ziad Oleimi, a prominent rights activist, told the crowds using a loudspeaker.
In Alexandria, some 10,000 opponents of Morsi gathered in the center of the country's second-largest metropolis, chanting slogans against the leader and his Islamic fundamentalist group, the Muslim Brotherhood.
The protests fueled Egypt's worst political crisis since Mubarak's ouster, with the country clearly divided into two camps: Morsi, his Muslim Brotherhood and their ultraconservative Islamist allies, versus an opposition made up of youth groups, liberal parties and large sectors of the public.
Tens of thousands also gathered in Cairo's downtown Tahrir Square, miles away from the palace, to join several hundred who have been camping out there for nearly two weeks. There were other large protests around the city.
Smaller protests by Morsi opponents were staged in the Islamist stronghold of Assiut, as well as in Suez, Luxor, Aswan, Damanhour and the industrial city of Mahallah, north of Cairo.
"Freedom or we die," chanted a crowd of several hundred outside a mosque in Cairo's Abbasiyah district. "Mohammed Morsi, illegitimate! Brotherhood, illegitimate!" they yelled.
Earlier Tuesday, several hundred protesters also gathered outside Morsi's residence in an upscale suburb. "Down with the sons of dogs. We are the power and we are the people," they chanted.
Morsi, who narrowly won the presidency in a June election, appeared to be in no mood for compromise.
A statement by his office said he met Tuesday with his deputy, his prime minister and several top Cabinet members to discuss preparations for the referendum. The statement suggested business as usual at the palace, despite the mass rally outside its doors.
Asked why Morsi did not address the crowds, Muslim Brotherhood spokesman Mahmoud Ghozlan said the protesters were "rude" and included "thugs and drug addicts."
The Islamists responded to the mass opposition protests last week by sending hundreds of thousands of supporters into Cairo's twin city of Giza on Saturday and across much of the country. Thousands also besieged Egypt's highest court, the Supreme Constitutional Court.
The court had been widely expected to declare the constitutional assembly that passed the draft charter illegitimate and to disband parliament's upper house, the Shura Council. Instead, the judges went on strike after they found their building under siege by protesters.
Morsi's Nov. 22 decrees were followed last week by the constitutional panel rushing through the draft constitution in a marathon, all-night session without the participation of liberal and Christian members. Only four women, all Islamists, attended the session.
The charter has been criticized for not protecting the rights of women and minority groups, and many journalists see it as restricting freedom of expression. Critics also say it empowers Islamic religious clerics by giving them a say over legislation, while some articles were seen as tailored to get rid of the Islamists' enemies.
Associated Press writer Maggie Michael contributed to this report.