Dozens of April 6 Youth Movement members gathered at the High Court in Cairo on Sunday morning to call for the release of detained activists and the removal of Prosecutor-General Talaat Abdullah who "lacks legitimacy."
The protesters are planning to conduct a sit-in and prevent Abdullah from entering his office inside the court building.
Last Wednesday, an appeal court reversed President Morsi's November 2012 decision to appoint Abdullah.
Opposition groups and analysts have said Abdullah should abide by the court ruling and resign from his post.
"We do not recognise him as the 'public prosecutor' after the court ruling and his intervention in favour of the ruling party by preventing the release of our members," April 6 media spokesman Khaled El-Masry said in televised comments on Sunday morning.
Protesters have locked the doors to the High Court with steel chains to prevent Abdullah entering his office, El-Masry said.
In the early hours of Sunday, fierce clashes broke out between April 6 members and dozens of street vendors and shop owners who forcibly dismantled tents erected for the planned sit-in.
Four April 6 members were injured by birdshot pellets, and gunshots were reported amid a complete absence of police, Al-Ahram Arabic news website reported.
Hundreds of April 6 members staged a protest outside the home of Interior Minister Mohamed Ibrahim at dawn on Friday to demand the release of 53 activists arrested in Tahrir Square on Wednesday.
At least four protesters were arrested at Friday's protest for chanting that the interior ministry was a “prostitute” and holding aloft women's underwear.
Meanwhile, dozens of supporters of Bassem Youssef also gathered at the High Court on Sunday morning. The satirist was issued with an arrest warrant on Saturday for allegedly insulting President Mohamed Morsi, denigrating Islam and spreading false news with the aim of disrupting public order.