The April 6 Youth Movement plans to stage an open sit-in in protest of the deployment of security forces and their use of violence against protesters downtown Tuesday night.
In an online statement, the group described the security reaction to protests by families of those killed during the revolution as "unfathomable and unconvincing". Security forces, which were deployed in large numbers, used tear gas and rubber bullets against those gathered in Tahrir Square.
The group said that the protests it had previously planned for 8 July will begin instead on Thursday following the dawn prayer.
April 6 also called on authorities to cease the escalation of violence and withdraw security forces from the square until the crisis is resolved.
It also urged the media to be fair in reporting the incidents, warning against a media blackout or other restrictions often imposed at state-run news outlets.
Prime Minister Essam Sharaf must open a comprehensive investigation into the events to punish those responsible or resign, the group said.
The group also urged authorities to more urgently prosecute former President Hosni Mubarak and cronies, abolish military trials for civilians, purge state institutions of officials who served under the former president, and abstain from infringing upon freedom of reporting and protesting.