The Sunni extremist group is at war with Iran-backed forces in Syria and Iraq.
The IS group often claims attacks around the world, even when links to the group can not be confirmed and appear dubious. It identified them only by their first names, saying it did not want to release their last names due to security and privacy concerns for their families.
The ministry also published pictures of their corpses.
Iran's Islamic Revolutionary Guard indirectly blamed Saudi Arabia for the attacks in a statement issued late Wednesday that also noted the "spilled blood of the innocent will not remain unavenged".
US President Donald Trump's response to the terrorist attacks in Iran has been denounced by Tehran as "repugnant". Foreign Minister Mohammad Javad Zarif in a tweet on Thursday called the White House comments "repugnant" and accused the USA of supporting terror.
At least 13 people were killed by the attackers, Iranian officials have said, while at least 43 others have been injured.
An Iranian MP later confirmed that the video showed his office and one of his employees lying dead.
During his recent trip to Saudi Arabia, Trump also called for a harder line against Iran advocating for the isolation of the country which he said had "fueled the fires of sectarian conflict and terror".
Supreme leader Ayatollah Ali Khamenei had yesterday said: "These fireworks have no effect on Iran".
Polls open in United Kingdom election after campaign marred by attacks
May was criticized for lackluster campaigning and deadly attacks that turned the election into a debate about national security. The 2015 elections saw the collapse of the Liberal Democrat vote, falling from 59 seats to their current nine seats.
The second attack, at the shrine of Ayatollah Ruhollah Khomeini, reportedly killed a security guard and wounded 12 other people.
Two teams of attackers used gunfire and explosives to strike Iran's parliament and the mausoleum of Ayatollah Khomeini in Tehran Wednesday, according to state media.
Police Thursday said they held a half dozen suspects in connection with the attacks.
"Our country always follows the course of preserving peace and stability in the region", said the Iranian embassy, noting that yesterday's terror attacks can be described as a reflection of the concern of enemies of peace in the region.
"One of the gunmen shot guard in the leg and ran away", it said.
Sen Bob Corker of Tennessee, the committee's Republican chairman and one of the bill's sponsors, said he recently reviewed top-secret intelligence that detailed Tehran's support for terrorism and other destabilizing actions.
Attackers dressed as women burst through parliament's main entrance in central Tehran on Wednesday, Zolfaghari said, according to the semi-official Tasnim news agency.
Gun ownership is tightly controlled in Iran, meaning those who carried out the attacks on the parliament and the shrine likely had to smuggle their weapons into the country.
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