A video on state television's website showed confused soldiers at the scene of the attack.
In the last decade, mass-casualty militant attacks have been incredibly rare.
Syrian President Bashar al-Assad and Hezbollah, two of Iran's closest allies, issued statements condemning the attack, with Assad referencing outside involvement and Hezbollah echoing allegations of U.S. blame.
It added that the terrorist crime committed in Ahvaz by the ruthless stooges of the global arrogance and reactionary regimes in the region revealed that the sworn enemies of Iran spare no effort and conspiracy to transfer insecurity into the country after their failure to achieve their ominous goals.
The State Department later offered a statement from spokeswoman Heather Nauert, who said that the US government was aware of the reports of an attack.
Meanwhile, an editorial by the daily's editor-in-chief Hossein Shariatmadari, who is appointed by Supreme Leader Ayatollah Ali Khamenei, threatened American, Israeli, Saudi, and UAE's military and security officials with retaliation.
But the semiofficial Tasnim news agency said at least eight IRGC members had been killed. Nine of those killed are reported to be members of Iran's Revolutionary Guard Corp, the semi-official ISNA news agency said.
The terrorist attack in Ahvaz, the capital of Khuzestan province, left 25 people, including women and children, dead.
Iran had enjoyed relative stability compared to Arab neighbours who have grappled with political and economic upheaval touched off by popular uprisings in 2011. The Islamic State group also claimed the attack, but initially offered incorrect information about it and provided no proof. Saudi Arabia has yet to respond to the allegations.
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Such attacks tend to unite Iranian reformers and hardliners despite sharp differences over domestic and foreign policies.
"The Persian Gulf states are providing monetary, military and political support for these groups", President Hassan Rouhani said before leaving Tehran to attend a UN General Assembly meeting in NY.
All four attackers were neutralized in the 10-minute gunfight.
Hardliners like the IRGC have gained standing at the expense of pragmatists in Iran's multi-tiered leadership since president Donald Trump decided in May to pull the United States out of the 2015 worldwide nuclear deal with Tehran and reimpose sanctions in moves to isolate the Islamic Republic.
Yahya Rahim Safavi, a senior Iranian Revolutionary Guards official, has vowed retaliation for the attack.
The Guards could put on a show of strength by firing missiles at opposition groups operating in Iraq or Syria that may be linked to the militants who staged the attack.
Rouhani could have been referring to Saudi Arabia, the United Arab Emirates or Bahrain, all of which are close U.S. military allies. In June 2017, coordinated assaults claimed by Islamic State on the country's parliament and the mausoleum of Ayatollah Ruhollah Khomeini killed 17 people.
Iranian soldiers jump over a hedge at a street as they run for cover during a terror attack that occurred during a military parade in the city of Ahvaz, southwest Iran, on Saturday.