The "White Ribbon national apology campaign" was launched on Wednesday following the alleged molestation of women marching in pro-reform demonstrations last week.
A group calling itself the Association of Egyptian Mothers had also asked all Egyptians to wear black on Wednesday as a symbolic public protest at the treatment of the women.
A sprinkling of Egyptians responded to the call.
The protesters were clad in black with white ribbons on their lapels to protest "police brutality, beating and sexual harassment".
They were waving banners demanding the resignation of Interior Minister Habib al-Adli and Cairo's head of security Nabil al-Ezabi, whom they hold responsible for the violence.
"Violating the dignity of women is like violating that of our country," and "our colleagues' dignity is part of the country's dignity," other banners read.
Calls for resignation
A group of 22 Egyptian human rights organisations issued a statement calling for al-Adli's resignation.
"The signatory organisations to this statement fear that Egypt is about to live one of the most violent periods in its history, when all independent voices will be targeted using the most malicious and dirty methods," the groups said.
Nawal Ali, one of the journalists allegedly sexually harassed, said she felt "comforted by this demonstration" as the crowd cheered her and gave her a hand.
Female activists protesting against the nature of the constitutional referendum submitted to Egyptians on 25 May and several female reporters covering the event were said to have been molested by civilian-clothed ruling party supporters.
Women journalists were among
The Egyptian government downplayed as "emotional tension" the beating and sexual groping of the women, some of which was caught on video.
The head of the Press Syndicate said the molestation was "a black page in Egypt's history".
At the demonstration, one man called President Hosni Mubarak's name and the crowd answered in unison "illegitimate".
Some in Egypt's opposition demanded that Mubarak quit office. The 72-year-old president has been in office for the last 24 years.
Thousands of policemen had deployed around the building, where last week's alleged molestations occurred, and on adjacent streets to prevent the protesters from marching in the capital.
Some 500 marchers were gathered on the syndicate's steps and another 500 inside the building.
Street demonstrations are banned under Egypt's emergency laws imposed after the assassination of President Hosni Mubarak's predecessor Anwar Sadat.