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".
Gen. Hossein Sajedinia told the semi-official ISNA news agency Wednesday night that police are interrogating the suspects.
Alavi says that many people in Iran and around the world believe Saudi Arabia supports Islamic militants across the region.
The six attackers "were Iranian and joined Daesh (IS) from some parts of Iran", said Reza Seifollahi, deputy secretary of Iran's Supreme National Security Council, on state TV late Wednesday. But no proof or specifics were offered.
The Islamic State claimed responsibility of the two attacks - a suicide bomb and gun assault - on the Iranian parliament and the mausoleum of the founder of the Islamic Republic.The ISIS media wing, Amaq, claimed "fighters with the Islamic State" carried out the assault.
Egypt's Foreign Ministry offered its condolences to the families of the deceased on Thursday and called on the global community to intensify its efforts to fight terrorism and its sources of funding.
Suicide bombers and gunmen attacked the Iranian parliament and Ayatollah Khomeini's mausoleum in Tehran, killing at least 13 people in an unprecedented assault that Iran's Revolutionary Guards blamed on regional rival Saudi Arabia.
Third London Bridge attacker named
It emerged that he was arrested past year trying to get into Syria, yet was still able to get into Britain, BBC reported. She said she tried to keep him away from radical friends, but "he had the internet and from there he got everything".
Shojaei earlier told state television that "three of the victims are women". Over 40 people were wounded in the attack.
The attack as politicians held a session in parliament and at the shrine of Ayatollah Ruhollah Khomeini shocked Iranians, who so far had avoided the chaos that has followed IS's rise in Syria and Iraq.
The ministry issued a statement on its website with bloody pictures of the men's bodies.
Due to security and privacy concerns for their families, the Ministry of Intelligence identified the terrorists only by their first names and did not disclose their last names.
The news agency, which put the death toll from the parliament attack at seven, also published an image of an alleged attacker displaying a hostage from a window.
Syrian President Bashar Assad has condemned the twin extremist attacks in Tehran, vowing the Iran and Syria would emerge victorious in their fight against "terrorism". Turkey's President Recep Tayyip Erdogan, center, Iranian Foreign Minister Mohammad Javad Zarif, left and Turkish Foreign Minister Mevlut Cavusoglu speak during a meeting in Ankara, Turkey, Wednesday, Jun.
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