Many of the protesters on Sunday had their mouths covered by yellow stickers reading "Enough".
Later, hundreds of security forces surrounded the offices of a veteran activist who had spoken out against the Mubaraks at the rally.
Some participants said the protest - held in front of Egypt's Supreme Judiciary Court - was the first purely anti-Mubarak protest since he came to power more than 23 years ago.
"Enough. No more extensions: No heredity: No succession," read one of the banners held by the protesters, who were cordoned off and outnumbered by riot police and senior police officials.
Call to leave
Following the protest, security forces surrounded the Socialist Studies Centre, where a seminar on change was being held, director Kamal Khalil said.
Khalil, a veteran activist, said hundreds of riot police and at least eight police trucks and an armoured car were outside his centre when he returned after the protest.
Khalil, 55, was one of the few people who spoke out at the demonstration.
The protest was organised by the
Egyptian Movement for Change
"Leave, enough," he chanted, addressing Mubarak. "This silent protest is against inheriting the ruling regime by Jamal Mubarak and against Mubarak's fifth term."
It was not clear whether the surrounding of Khalil's office was related to his remarks at the protest.
"I'm not worried or afraid. This is a despotic and repressive country," Khalil said by telephone from inside the centre.
"I really don't care if they arrest me after the seminar, I will continue to defend my ideas and principles, even if surrounded by a million tanks."
Khalil said he has been arrested more than 15 times since 1968.
Islamists, nationalists, those on the left and liberals all joined the protest, organised by the Egyptian Movement for Change, a group made up of political parties and intellectuals, to press their demand for a constitutional change to allow more than one candidate to run for president.
"This is a historic protest," Majdi Ahmad Husain, a member of the Islamic political movement, said.
"This is the first protest demanding ending his rule. The demonstration's meaning is bigger than its size. We've entered a new phase."
During the past two years, participants at rallies in support for Palestinians and Iraqis have also chanted anti-Mubarak and anti-Jamal Mubarak slogans.
President since 1981, Mubarak's
current term ends in late 2005
Mubarak, 76, has been Egypt's president since replacing his assassinated predecessor, Anwar al-Sadat in 1981. His current six-year term ends in October 2005, and he has not said whether or not he will run again.
Mubarak has never had a vice-president. There has been strong speculation in recent years that Mubarak's son Jamal, 41, is being groomed as his successor.
Egypt holds presidential referendums, rather than elections, in which people vote "yes" or "no" for a sole candidate.
In October, more than 650 people - Islamists, communists and 30 lawmakers - signed a petition demanding an amendment to Egypt's constitution that would limit a president to two terms.
On Sunday, the protesters dispersed peacefully within an hour, singing a revised version of the Egyptian national anthem: "My country, you still have oppression in politics and economics, you need revolution, my country."
The real lyrics are: "My country, you have my love and my heart."