The interior ministry issued a statement yesterday evening identifying the men as Hassan Ben Khalifa Bouchiba, Houcine Ben Khalifa Bouchiba and Walid Ben Mohamed Ali Yousfi.
An initial probe has proven that these "terrorist elements... (are) linked to the explosion on a bus of the presidential guard," the statement said.
The ministry also promised "an important financial reward" for "anyone providing information leading to the arrest" of the three suspects.
Tuesday's suicide bombing in the centre of Tunis was claimed by the Islamic State group, and authorities have identified the bomber as 26-year-old Tunisian travelling salesman Houssam Abdelli.
However, the prosecution decided that he should be kept under surveillance but it is not clear if any surveillance was ever carried out. The police report into the August incident only reached the prosecutor's office on Thursday, two days after the attack.
The interior ministry said today it had carried out hundreds of searches and arrested dozens of people since the attack, of whom "41 people suspected of belonging to terrorist organisations" were detained overnight.
The secretary of state for national security, Rafik Chelly, told private Mosaique FM radio that all these attacks were planned in neighbouring Libya.
Tunisia, the cradle of the Arab Spring uprisings, has been plagued by Islamist violence since the 2011 overthrow of longtime dictator Zine El Abidine Ben Ali.
IS has exploited the chaos that spread across Libya since the 2011 revolt that toppled and killed veteran leader Muammar Gaddafi to gain a presence in the oil-rich North African state.
