The television said there was a "tangible" presence of "terrorists" with firearms and explosives during the riots in the central Tehran neighbourhoods of Enghelab and Azadi.
"Unfortunately, in the riots that ended up with clashes, 10 people were killed and more than 100 people were wounded," it said.
Iran's deputy police chief Ahmad Reza Radan blamed the exiled opposition group the People's Mujahedeen of Iran (PMOI) of being behind Saturday's violence, the television said.
"The infiltrated thugs and agents of the MKO (Mujahedeen Khalq Organisation) among the crowd... used firearms which were the reason for the casualties," he said referring to the PMOI.
The official IRNA news agency said that Iran had arrested several members of the PMOI over their alleged role in the post-election riots.
Iran's intelligence ministry arrested an unspecified number of the group's militants for carrying out "terrorist actions" after the June 12 poll, the report said, without giving a source.
The ministry has "identified and arrested a number of hypocrites who were trained in Ashraf camp in Iraq and entered Iran in order to carry out terrorist actions," IRNA said.
"Those arrested have confessed that after receiving training in Iraq, they entered Iran and were commanded and supported by the hypocrites in Britain," the report added.
Founded in 1965 with the aim of overthrowing the US-backed shah and then the Islamic regime, the PMOI has in the past operated an armed group inside Iran.
It was the armed wing of the France-based National Council of Resistance of Iran (NCRI) but it renounced violence in June 2001.
Ashraf, a camp in Iraq close to the Iranian border, houses around 3,500 PMOI members.
Tehran has been rocked by violent protests since incumbent President Mahmoud Ahmadinejad was declared the winner of the June 12 vote, which the opposition claims was rigged.
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