In Tahrir, demonstrators chanted against the ruling military council and vowed to keep their revolution alive. “Revolutionaries, free, we will continue our journey,” they chanted.
Mubarak, 84, and his interior minister Habib al-Adly were sentenced to life in prison on Saturday, but six security chiefs were acquitted of the killings of demonstrators during last year's uprising that left some 850 people dead and ousted the veteran president.
The ruling sparked nationwide outrage, with thousands taking to the streets to vent their rage that no one had been found directly guilty of killing the protesters.
“We want a just ruling in the trial of Mubarak and the police chiefs,” said Abdel Wahab, a builder who belongs to the Muslim Brotherhood.
Mubarak — the only autocrat toppled in the Arab Spring to be put in the dock — could have been sent to the gallows as demanded by the prosecution but was instead given a life term, angering many.
He was also cleared of graft charges.
Along with the acquitted police chiefs, Mubarak's sons Alaa and Gamal had corruption charges against them dropped on a technicality, but they will remain in custody pending trial on other graft charges.
“We reject the trial. It's a big farce,” said Hisham Khalifa, 30, inTahrir Square.
He said demonstrators also wanted the dismissal of the prosecutor general “who has ignored many corruption cases.”Demonstrators also want the implementation of a law that would see senior Mubarak-era figures barred from standing for public office.Egypt's top court has still to rule on the law's constitutionality.
The legislation could have serious implications for Ahmed Shafiq, Mubarak's last prime minister, who is due to face the Muslim Brotherhood's Mohammed Mursi in a presidential election runoff next week.
“We would accept to vote for Mohammed Mursi on condition that he accepts vice presidents and a prime minister from other groups,” said Ayman Mohammed.
Behind him, some protesters wore badges urging people to boycott the vote.
Tuesday's protest was called by youth groups which were a driving force behind the uprising against Mubarak's regime last year, including the Coalition of Revolution Youth and the Maspero Youth Union. It also received the backing of the Muslim Brotherhood.
The runners-up in the first round of the presidential election, leftist politician Sabbahi and moderate Abul Fotouh, led separate marches toTahrir Square.
They came third and fourth respectively in the May 23-24 first round.
“We believe that our revolution is not over. The military must leave power and hand it to civilians,” said Mahmud Bahira, a protester from the Revolution Youth movement.
Another protester Mohammed Shabik said: “The judgement in the Mubarak case is not tough enough, there are even people who have been acquitted.”Egypt's prosecutor has said that the verdicts will be appealed, but a judicial source said that the process would take several weeks.
Mubarak's defence team has also said it will challenge the verdict and told AFP it was confident of winning on appeal. The verdicts come just two weeks before the presidential election runoff which is becoming highly polarised with many activists facing a difficult choice.
For activists, choosing Shafiq, a Mubarak-era figure, would symbolise a return to the old regime and an end to the revolution, but voting for Mursi would mean handingEgyptto a movement they say has monopolised power since the uprising.