Authorities said the death count had risen to 17 and scores were wounded.
If the IS claim is true, the bomb and gun attack would be the group's first successful attack in Iran, which is predominantly Shiite Muslim and regarded by Sunni militants as a nation of heretics.
Authorities said five Iranians, who had joined IS and travelled to its Iraq and Syria bastions, carried out Wednesday's attacks on the parliament and the shrine of revolutionary leader Ayatollah Ruhollah Khomeini.
Iran has blamed Saudi Arabia, citing statements made against the Islamic Republic by the kingdom's foreign minister and deputy crown prince as having instigated the attacks.
The Saudi's have denied involvement in the attack.
The statement said Saudi Arabia "constantly supports" terrorists including the Islamic State group, adding that the IS claim of responsibility "reveals (Saudi Arabia's) hand in this barbaric action".
Iran's supreme leader, Ayatollah Ali Khamenei, said the attacks will add to the hatred that Iranians harbor toward the USA and Saudi Arabia.
Alavi also added that the safe house used by the five terrorists who carried out the attacks in Tehran was discovered by security forces and the brother of one the terrorists, who according to the minister was even more risky, was caught by the intelligence forces.
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The ministry also published pictures of their corpses. You know we are crying for people in Syria, it's not that all Iranians are fighting in Syria.
Iran arrested another seven linked to the recent deadly terrorist attacks in the capital Tehran, local media reported on Saturday.
The Parliament assault began when four armed assailants, dressed as women, burst into the building complex and attacked the parliament buildings in the morning, reports Tasnim news.
Trump had said he prayed for the victims of Wednesday's attacks that were claimed by Islamic State, but added that "states that sponsor terrorism risk falling victim to the evil they promote". Iran also has been fiercely opposed to the militant group.
ISIS released a video overnight of the five attackers before the assault, via its Amaq propaganda agency. According to a statement by Iran's Intelligence Ministry, a large number of documents, and devices used by terrorists, were also confiscated.
Since U.S. President Donald Trump took office in January, the yawning gap between Tehran and Washington has grown even wider with Trump's latest efforts to isolate Iran in the region, while bolstering cooperation with Saudi Arabia and the Gulf countries.
"In this bill, filled entirely with the support of terrorism, they have imposed sanctions on Iran's missile technology, IRGC and the Quds Force".
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