"Enough!" said one banner, in an apparent reference to Mubarak's 24-year rule in Egypt and his expected decision to run for a sixth term later this year.
"No to the renewal (of Mubarak's mandate)," shouted some demonstrators near a mosque during a book fair in the Egyptian capital.
"No to heredity," referring to speculation that if Mubarak does not stand his eldest son, Jamal, will be become president instead.
Under the Egyptian system, parliament will elect in May a candidate to stand for the presidency, who will subsequently be put for approval to the people at a referendum in September.
The opposition has long called for constitutional reform to allow the president to be chosen from a list of candidates by universal suffrage.
Rights group's appeal
Also on Friday, Human Rights Watch said Egypt should set free a lawmaker, a journalist and several others arrested on "politically motivated charges" and stop harassment of peaceful dissidents.
"The government has arrested and banned these critics simply for exercising their rights to freedom of speech and assembly and association," said Sarah Leah Whitson, Middle East director at Human Rights Watch, in a letter sent on Friday to President Husni Mubarak.
"The authorities should release them from custody at once and put an end to these repressive tactics," she said.
Beside the arrests of parliament member Ayman Nur, a journalist, a lawyer, a student and nine members of the banned but tolerated Muslim Brotherhood late last month, Egyptian authorities also raided a book fair and banned a planned appearance there of Muhammad al-Said, deputy director of the Al-Ahram Center for Political and Strategic Studies, after he publicly called for constitutional reform.
The arrests dashed hopes "that Egypt was turning a new page on human rights" when the government allowed a public demonstration against Mubarak in December, the New York-based rights group said.
Egypt's "radical crackdown on peaceful dissent sends the message that there's no place for democratic freedoms under Mubarak," added the group.
"The Egyptian government should immediately release ... peaceful critics arrested in recent days on politically motivated charges," the group said, adding that Mubarak "should instruct security officials to cease the systematic harassment and intimidation of peaceful dissidents."