The cell members were caught near Sarbaz in the southeast, said a statement from Iran's elite Revolutionary Guards (IRGC) published by the official IRNA news agency.
The report said those detained had "committed a series of terrorist attacks, including the killing of teachers and Basij (Islamic militia volunteers)."
Sarbaz is in Sistan-Baluchistan province, which borders Pakistan and has a large Sunni community. It is plagued by violence involving Sunni extremists and drug smugglers.
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Iran accuses members of the Sunni militant group Jaish-ul Adl (Army of Justice) of carrying out frequent raids.
Sistan-Baluchistan police chief General Hossein Rahimi told state television that the 12 cell members were arrested by security forces on Saturday night.
They admitted to killing a teacher and Basij members as well as two municipal employees, and also owned up to an ambush last week that killed three Iranian soldiers near the Pakistan border, Rahimi said.
In a separate incident, three Afghan nationals carrying explosives were arrested by border police close to Iraq, said the semi-official Fars news agency, considered close to the IRGC.
They had crossed into Iran and intended to join the Islamic State group in Iraq when they were detained, Brigadier General Qassem Rezayee of the Border Force told Fars.