Footage on social media showed soldiers and bystanders scattering as shooting broke out at the parade in Ahvaz marking the 38th anniversary of Iraq's 1980 invasion of Iran. "Iran holds regional terror sponsors and their USA masters accountable for such attacks".
The attack took place on a day when military parades were being staged across the country to mark the anniversary of Iran's eight-year war with Iraq in the 1980s.
Foreign Minister Mohammad Javad Zarif said Iran will respond "swiftly and decisively" to the attack, holding agents of a foreign regime responsible.
Pointing to the media war against Iran claiming that Iran trains and funds terrorists, Shekarchi said today's terrorist attack and the brutal massacure of innocent people, children, disabled war veterans and soldiers prove that the Islamic Republic of Iran itself is the victim of terrorism.
Two gunmen were killed and two others were arrested, reports quoted the governor as saying.
While the identities of the attackers remained unclear, a spokesman for Iran's Revolutionary Guard Corps blamed minority Arab separatists for the bloodshed.
Iranian Supreme Leader Ayatollah Ali Khamenei accused USA -backed Gulf Arab states of carrying out an attack on a military parade that killed 25 people, nearly half of them members of the country's elite Revolutionary Guards.
Fars news agency said the attack started at 09:00 local time (06:30 BST), lasted about 10 minutes, and appeared to involve four gunmen.
A spokesman for the so-called Ahvaz National Resistance said the group was behind the attack.
The state-run IRNA news agency said a woman and a child were also among the wounded.
The Islamic State group also claimed responsibility in a message on its Amaaq news agency, but provided no evidence it carried out the assault and initially wrongly said the attack targeted President Hassan Rouhani, who was in Tehran. Iran has blamed its Mideast archrival, the Sunni kingdom of Saudi Arabia, for funding their activity.
Iran will face pressure to respond to the high-profile attack on the Revolutionary Guards, the strategic force with the greatest commitment to the clerical leadership.
State television immediately described the assailants as "takfiri gunmen", a term previously used to describe the Islamic State group.
The statement was posted on Amaq accounts on on messaging application Telegram.
If it was IS, it would represent a failure by Iran's intelligence community to prevent a second major IS attack in its soil.
In a keynote speech, Rouhani vowed to boost Iran s ballistic missile capabilities despite Western concerns that were cited by his USA counterpart Donald Trump in May when he abandoned a landmark nuclear deal with Tehran.
"Iran neither put its defensive arms aside nor lessens its defensive capabilities", Rouhani said. "The fact that the missiles anger you shows they are our most effective weapons", he said, referring to the West.
Iran has ballistic missiles with a range of up to 3,500 kilometres (2,200 miles), enough to reach both Israel and US bases in the Middle East.