Iran says the attackers who killed 12 people in the capital Tehran were Iranians who had joined so-called Islamic State.
Iran’s powerful Revolutionary Guards accused Saudi Arabia and the US of being behind the attacks.
The violence comes amid heightened tension in the Middle East, with Saudi Arabia and other Arab states cutting ties with Qatar over alleged support for Islamist militants and closer ties with Iran.
Sunni-ruled Saudi Arabia and Shia-majority Iran are staunch regional rivals.
In an interview on state TV, Reza Seifollahi, deputy chief of Iran’s Supreme National Security Council, said the attackers “Had joined Daesh [IS] from a number of regions inside Iran.”.
IS earlier claimed the attacks – a first for Iran – and threatened further assaults on Iranian Shia Muslims.
Iran’s Revolutionary Guards vowed revenge for the bloodshed, but pointed the finger at the US and Saudi Arabia in the wake of President Donald Trump’s recent visit to the kingdom.
BBC Persian’s Jenny Norton says that despite Iran’s active involvement in fighting IS in both Iraq and Syria, the Sunni group has not until now carried out any attacks inside Iran, and appears to have little support in this predominantly Shia country.