The deputy head of the Revolutionary Guards meanwhile warned the United States and Israel to expect a "devastating" response, accusing them of involvement.
"Terrorists began shooting from a long distance while inside the park, at the armed forces as well as civilians watching the parade", Brig.
"They are not from Daesh [ISIS] or other groups fighting [Iran's] Islamic system", Brig Gen Abolfazl Shekarchi told the official news agency IRNA.
A video circulating on the ISIS-affiliated Amaq News Agency claims to show three of the four assailants accused of carrying out a deadly terrorist attack on an Iranian military parade.
Because numerous Ahvaz Arab opposition groups in Khuzestan province are made up of Shi'ites it would be odd for them to join an ISIS group. Iranian media has highlighted the involvement of Saudi Arabia, gulf countries, the UK, Denmark and Holland in hosting or supporting Ahvaz opposition groups.
Of those killed, at least eight are believed to be members of Iran's elite Revolutionary Guard.
IRGC spokesman Ramezan Sharif said the attackers were affiliated with a terrorist group supported by Saudi Arabia, Iran's state-run Press TV said.
Rouhani said: "The small puppet countries in the region are backed by America, and the United States is provoking them and giving them the necessary capabilities". Saudi Arabia has yet to respond to the allegations.
Islamic State also bragged that it staged the carnage, but Tehran denied the claim outright. It also said that the attackers had ties to Israeli intelligence Mossad.
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Khuzestan, which has a large ethnic Sunni Arab community, was a major battleground of the 1980s war with Iraq and it saw unrest in 2005 and 2011, but has since been largely quiet.
Many held pictures of a four year old boy killed in the attack, one of the worst against the most powerful military force of the Islamic Republic.
He added that Iran would voice its views on "the global situation" at the United Nations, adding: "The US showed the world their bullying nature and they keep continuing their unilateral policies".
This combination of two pictures shows U.S. President Donald Trump, left, on July 22, 2018, and Iranian President Hassan Rouhani on February 6, 2018.
The Trump administration announced earlier this week, it's actively looking to negotiate a new deal with Iran to curb its nuclear weapons and missile program.
"Rather it will increase its defense power day by day".
Following the assault, Iran openly blamed the U.S. and its Gulf allies for backing the attackers. We've always stood by that... "We hope that the backers, financers and proponents of terrorism will understand that this danger threatens mankind as a whole".
Armed men conducted the attack in the southwestern city of Ahvaz, according to Iranian state television. In 2009, more than 40 people, including six Guard commanders, were killed in a suicide attack by Sunni extremists in Iran's Sistan and Baluchistan province.
The attack on the military parade is likely to give security hardliners like the Guards more political ammunition because they did not endorse the pragmatist Rouhani's pursuit of the nuclear deal with the West, analysts say.