On Thursday, authorities said the assailants were Iranian nationals and they had arrested six suspects, including one woman, since the attacks.
Iranian leaders, meanwhile, accused the United States and Saudi Arabia of supporting the attacks, which killed 17 people in Tehran.
Iran's Intelligence Ministry has confirmed that five of the men involved in terror attacks in Iran had fought for the Islamic State group.
The statement also said the attackers had first returned to Iran in July-August 2016 as part of a network intending "to carry out terrorist operations in religious cities", but were forced to flee after their cell was dismantled. The Islamic State group claimed the attacks.
Publicly, the Iranian leadership has sought to cast blame for the attacks on its favorite targets: Saudi Arabia, the United States and Israel.
He called regional rival Saudi Arabia "a tribal state very far from anything like a democracy", and denounced U.S. sanctions against Iran over its ballistic missile programme. There have been attacks on the Saudi security forces and the country's minority Shiite population and on Medina- one of the holiest sites in Islam.
Saudi Arabia, Gulf allies hail Donald Trump's remarks on isolated Qatar
Ankara has worked alongside Qatar to support Islamist groups and militias in Syria and elsewhere. The Arab states have also ordered Qataris out within 14 days.
Egypt has condemned Islamic State-claimed attacks on Iran's parliament and a shrine to its revolutionary leader in the "strongest terms".
On a recent trip to Sunni-ruled Saudi Arabia, Trump called on all nations to "isolate" Iran.
A senior official, who also asked not to be named, said the attacks would push Iran toward "a harsher regional policy".
Intelligence Minister Mahmoud Alavi has said Iran identified several jihadists, where they meet and where they hide.
The intelligence ministry said Friday 41 suspects were arrested in Tehran, in the northwestern provinces of Kermanshah and Kurdistan, and in West Azerbaijan, near the borders with Iraq and Turkey.
Security forces have found explosive vests and other equipment, as well as an abandoned vehicle, packed with at least 22 pistols, in Kermanshah province.
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