A third protest at the Sunni al-Azhar mosque was originally planned to demand that the al-Aqsa mosque in Jerusalem remain out of Israeli control. But the gathering turned into a Muslim Brotherhood call for speedy parliamentary elections, the BBC reported.
Protesters in Tahrir Square called the demonstration "Last-Chance Friday." Instead of police using tear gas, a feature of recent demonstrations in the square, peddlers sold toffee apples and tea.
Many of those in the square, which has been the focus of anti-government protest all year, want parliamentary elections postponed, the BBC said. One student said that following the police crackdown many are afraid to go to the polls.
Most of those in Tahrir do not accept the appointment of Kamal Ganzouri, who headed Egypt's government under Mubarak from 1996 to 1999, to form a new government following this week's resignation of the whole Cabinet to protest the latest military crackdown on protesters, the BBC said.
Thousands of people also rallied near the headquarters of the Supreme Council of the Armed Forces. They held signs that read "Down with Tahrir Square" and "Tahrir does not represent Egyptians."
British newspaper The Daily Telegraph reported the 78-year-old Ganzouri's appointment, announced on television Friday, came after he met with military leader Field Marshal Hussein Tantawi late Thursday.
Ganzouri replaces Essam Sharaf, who resigned this week amid violent clashes between police and protesters.
The transition to civilian rule is being overseen by the Supreme Council of the Armed Forces. But despite its pledge to speed the process, some protesters worry the council wants to stay in power and are seeking an end to military rule before parliamentary elections are held.
But other Egyptians, including the Muslim Brotherhood, which is expected to do well in the vote, want the polls to go ahead as planned.
In Washington, the White House called for a transfer of power to civilians "as soon as possible."
"The United States strongly believes that the new Egyptian government must be empowered with real authority immediately," a White House statement said.