Scores of people were also wounded.
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". A senior Interior Ministry official told Iran's state TV the male attackers wore women's attire. At least one was disguised as a woman, according to witnesses.
Parliament Speaker Ali Larijani called the attacks a cowardly act.
All the attackers were killed.
The attack came as emboldened Sunni Arab states - backed by U.S. President Donald Trump - are hardening their stance against Shiite-ruled Iran.
State Department spokeswoman Heather Nauert said the USA expressed condolences to the victims and their families.
The militants released a graphic video of the attack. By Allah, we will strike you in your own homes. "We are here to stay, God willing".
Meanwhile, President Trump's statement on the attack has prompted criticism in Iran.
Iran is a majority-Shiite nation, and the Islamic State is a Sunni group that often targets Shiite Muslims.
The assault drew swift condemnation and expressions of condolence from countries such as Syria, Pakistan and Russian Federation.
It then added, "We underscore that states that sponsor terrorism risk falling victim to the evil they promote".
But Intelligence Minister Mahmoud Alavi said on Thursday that "we still can not judge that Saudi Arabia has had a role in this terrorist incident".
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Iran has indirectly suggested that Saudi Arabia, its major regional rival and a US ally, played a role in the attack. According to a statement from the Fars news agency, Iran "sees the fact that this terrorist act was perpetrated soon after the meeting of the U.S. president with the heads of one of the reactionary regional states that has always supported". Is enabling that worth scoring a point on Iran?
Even as Washington expressed its condolences on Wednesday, the US Senate advanced legislation that would impose new sanctions on Iran, partly for what the bill described as the Iranian regime's "support for acts of global terrorism".
Iran's supreme leader, Ali Khamenei, played down the significance of the attacks, saying, "These fireworks have no impact on the will power of the people". That's Anti-War 101. No reason why it shouldn't apply to Iran's adventures in Syria as much as to America's adventures in Iraq.
The huge turnout was described as a national festivity and won global praise. Commuters in the Iranian capital noticed more police than usual on the streets as dawn broke.
The siege at parliament lasted about three hours, and it appeared that not all lawmakers were aware of the extent of the violence at first. It said they returned to Iran in August under the command of an Islamic State leader and escaped when authorities initially broke up their extremist cell. "We continued. discussions until 1 p.m., when we heard the shooting".
Two Sunni militant groups, Jaish al-Adl and Jundallah, have been also waging an insurgency in Iran, mostly in remote areas, for nearly a decade.
The attacks drew condemnation and condolence from the governments of Pakistan and from Iran's close allies in the Russian and Syrian governments.
"The terrorist wrapped up in a black chador and carrying a gun entered, shot the gate guard and opened the gate for his fellow terrorists", Falahatpishe said.
The comments sparked anger from Iranians on social media, who recalled the vigils in Tehran that followed the September 11 attacks.
Five of the attackers died and, Reuters reports, more than half a dozen suspects have been arrested in connection with the assault - the first major attack Iran has experienced in years.
The statement further added that several houses used by Wahhabi-Takfiri terrorists were identified in northwestern parts of the country and cleared of the terrorists.
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