The two simultaneous attacks were carried out by IS militants in Iran's Majlis (parliament) and the mausoleum of the founder of the Islamic republic Ayatollah Khomeini.
The men who made their way through the parliament building Wednesday were probably Iranian Kurds, security sources say, though only one has been identified.
Saudi Arabia dismissed the accusation. It stopped short of directly blaming the kingdom for the attack.
The men had left Iran to fight for the extremist group in Mosul, Iraq, as well as Raqqa, Syria - the group's de facto capital, the ministry said.
"For these two actions to happen. after this meeting means that the U.S. and Saudi regimes had ordered their stooges to do this", said Mohammad Hossein Nejat, deputy head of the Revolutionary Guards intelligence branch, according to the Fars news agency.
The state-run IRNA news agency reported the increase Thursday, citing Ahmad Shojaei, the head of the country's forensic center.
State Department spokeswoman Heather Nauert had said the U.S.is sending thoughts and prayers to the Iranian people following the attacks.
Austrian Foreign Minister Sebastian Kurz was also among senior diplomats condemning the terrorist attacks in the Iranian capital.
They entered Iran previous year under the command of Abu Aisha al-Kurdi, a ringleader of the ISIS terrorist group to carry out terror attacks in Iran's religious cities, according to the ministry.
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Trump had said he prayed for the victims of Wednesday's attacks that were claimed by Daesh, but added that "states that sponsor terrorism risk falling victim to the evil they promote".
Islamic State claimed responsibility and threatened more attacks against Iran's majority Shiah population, seen by the hardline Sunni militants as heretics.
Meanwhile, another attack took place at the Imam Khomeini Shrine.
Iran's Revolutionary Guards have suggested that the attack was linked to Saudi Arabia.
Tehran police said the vehicle the attackers used for both attacks was discovered on Saturday in the city centre.
Recent IS propaganda underscores that point too; they have called on Iranian Sunnis to rise up against the Iranian government and ratcheted up their usual attacks on them as well.
Lifting economic sanctions saved Iran's economy, GOP lawmakers added, and allowed the country to funnel more money to terrorist groups.
The comments sparked anger from Iranians on social media, who recalled the vigils in Tehran that followed the September 11 attacks.
Another official said the attackers were dressed as women and entered through the visitors' entrance. In this photo released by an official website of the office of the Iranian supreme leader, Supreme Leader Ayatollah Ali Khamenei addresses a group of students in Tehran, Iran, Wednesday, June 7, 2017. The.
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