The state-run IRNA news agency put the number of wounded at 20, including a woman and a child.
Earlier reports on Saturday described the assailants as Takfiri, a term previously used to describe Islamic State.
Meantime, media reports said that the Al-Ahvaziya terrorist group has claimed responsibility for the attack.
Khuzestan was a major battleground of the 1980s war with Saddam's Iraq and the attack on the anniversary parade in Ahvaz had significant symbolic value.
The bloodshed struck a blow to security in OPEC oil producer Iran, which has been relatively stable compared with neighbouring Arab countries that have grappled with upheaval since the 2011 uprisings across the Middle East.
The Revolutionary Guard is a paramilitary force answerable only to Supreme Leader Ayatollah Ali Khamenei.
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An official carries a child after gunmen attacked a military parade in the Iranian city of Ahvaz, that killed 24 and injured 53.
Foreign Minister Mohammad Javad Zarif says Iran will respond "swiftly and decisively" in defense of its people, shortly after a terror attack claimed at least 10 lives in southern Iran. In it, paramedics could be seen helping someone in military fatigues laying on the ground.
However, Iran faced a bloody assault a year ago from the Islamic State group and Arab separatists in the region have attacked oil pipelines there in the past.
The Islamic Revolution Guards Corps (IRGC) spokesman Ramezan Sharif said the attackers were affiliated to a terrorist group supported by Saudi Arabia. However, Arab separatist groups in the region have launched attacks on oil pipelines there.
The semi-official ISNA news agency published photographs of bloodied troops in dress uniforms helping each other walk away on Quds, or Jerusalem, Boulevard in Ahvaz.
State television said the attack targeted a stand where officials were gathered to watch the annual event, marking the start of the country's 1980-88 war with Iraq. The assault shocked Tehran, which has seen few militant attacks in the decades after the tumult surrounding the Islamic Revolution.