The arrests were made in Alborz province's Fardis town, reports Xinhua news agency.
Tehran police said the auto the attackers used for both attacks was discovered on Saturday in the city centre.
On June 9, Iranian authorities announced that they had detained 41 suspects in connection with the attacks.
Two guards, 10 government staffers and five civilians were killed in the attacks that simultaneously targeted the country's parliament and shrine of late founder of the Islamic Republic Ayatollah Ruhollah Khomeini.
The death toll from Wednesday's incidents in Tehran grew to 17, while more than 40 others were wounded. Find us on Facebook too!
As thousands of Iranians attended a funeral for the victims, Supreme Leader Ayatollah Ali Khamenei said Wednesday's attacks would only increase hate for the USA and Saudi governments, according to state media.
The Islamic State has claimed responsibility for the attacks.
IS has long vowed to attack Iran because the country had deployed military advisers and support to both Syria and Iraq in their fights against the extremist group. Times staff reporter Hennessy-Fiske reported from Beirut.
The cutting remarks from Khamenei came one day after Iran's foreign minister, Mohammad Javad Zarif, denounced President Trump's response to the suicide bombing as "repugnant".
On Friday, the US embassy in Saudi Arabia issued a security notice to USA citizens recommending that they "exercise caution in places frequented by foreigners due to the continuing risk of terrorist attacks. across the Kingdom". Plainclothes agents, recognizable by their government-issued walkie-talkies, paced up and down the streets, stopping anyone who looked out of the ordinary.