Prosecutor General Talaat Ibrahim Abdallah has authorized the arrest “of all people suspected of belonging to the group and ordered that they be brought before the courts,” the source said.
The demonstrators, their faces hidden by black masks, have appeared among stone-throwing protesters during the deadly riots which have rocked Egypt since Thursday.
“Inquiries have shown that the Black Bloc is an organized group which carries out terrorist actions,” said the prosecutor general’s spokesman Hassan Yassine.
The prosecutor urged “citizens to arrest anyone suspected of membership in this group and hand them over” to the army or the police, said Yassine.
And he also decided to appoint a judge to investigate a complaint lodged by a lawyer who accused the Black Bloc of torching Muslim Brotherhood offices, and of links to opposition and media figures, he added.
Presenting themselves as the defenders of protesters opposed to Mohamed Mursi’s rule against the president’s Muslim Brotherhood supporters, they reportedly model themselves on anarchist groups of the same name in Europe and the United States.
In a video posted on YouTube, the militants say they want to “confront the regime of the fascist tyrants” -- a reference to the Muslim Brotherhood of which Mursi hails.
Photographs showed them celebrating around a police armored vehicle in flames in the middle of Tahrir Square this week, waving V-for-victory signs.
The origins and leadership of the group is shrouded in mystery and the extent of its membership unknown.
At least 52 people have died in the latest wave of violence, which first erupted on Thursday.
It gained momentum on Friday, when protests marking the second anniversary of the start of the uprising that toppled long-time president Hosni Mubarak turned into clashes around the country.
On Saturday, violence exploded in Port Said after a court sentenced to death 21 supporters of a local football club for their involvement in a deadly soccer riot last year.