"The five known terrorists... After joining the Daesh (IS) terrorist group, left the country and participated in crimes carried out by this terrorist group in Mosul and Raqa," the ministry said in a statement.
The statement indicates only five people carried out yesterday's twin attacks, rather than six originally reported.
The ministry released images and the first names of the dead attackers, who killed 17 people and wounded dozens in gun and bomb assaults on Tehran's parliamentary complex and the shrine of revolutionary founder Ayatollah Ruhollah Khomeini yesterday.
Abu Aisha was killed and the network forced to flee the country, the statement said.
It was not clear when the five men returned to Iran ahead of yesterday's attacks.