The separatist group the Patriotic Arab Democratic Movement in Ahwaz claimed responsibility for this attack.
The group is supported by "foreign antagonists," including Saudi Arabia, IRNA said.
"The terrorists disguised as Islamic Revolution Guards Corps (IRGC) and Basiji (volunteer) forces opened fire to the authority and people from behind the stand during the parade," Governor of Khuzestan Gholam-Reza Shariati said, according to IRNA.
IRGC spokesman Ramezan Sharif said the attackers were affiliated with a terrorist group supported by Saudi Arabia, Press TV said. "The individuals who fired at the people and the armed forces during the parade are connected to the al-Ahvaziya group which is fed by Saudi Arabia," Sharif said. Saudi Arabia has yet to respond to the allegations.
The parade was part of nationwide celebrations in Iran to mark the 30th anniversary since the end of the eight-year war with Iraq that started in September 1980 and ended in August 1988.
The attack happened in a province bordering Iraq that has a large ethnic Arab community, many of them Sunni. It was a major battleground during the war that killed half a million soldiers.
According to the Iranian state news agency IRNA 24 people, including a journalist, have been killed in a terrorist attack at a military parade in Iran, while 21 others have been injured, according to the Tasnim News Agency.
Iran will respond "swiftly and decisively" to an attack on southwestern Iran, Iranian Foreign Minister Mohammad Javad Zarif said.
"Terrorists recruited, trained, armed & paid by a foreign regime have attacked Ahvaz," Javad Zarif tweeted. "Iran will respond swiftly and decisively in defense of Iranian lives."
According to the political deputy governor of Khuzestan Province, Ali Hossein Hosseinzadeh, "the blind and coward terrorist attack" claimed lives of 10 people, including a journalist, Tasnim News Agency reported.
A total of 21 others were injured, Hosseinzadeh said, noting that death toll was likely to rise as some of the victims were in critical condition.
According to the IRNA news agency, 20 people have been wounded; the number of killed has yet to be reported.
At least 8 Islamic Revolutionary Guard Corps (IRGC) personnel have been killed in the terrorist attack that hit a military parade in the southern Iranian city of Ahvaz on Saturday, Press TV channel reported.
According to Tasnim News Agency, between eight and 10 IRGC personnel were killed in the attack, with seven others injured.
"Shooting began by several gunmen from behind the stand during the parade. There are several killed and injured," a correspondent told Iranian state television.
Two militants were reportedly killed by the security forces, while two others are still at large.
Iranian state news agency Tasnim has reported that Takfiri terrorists opened fire at people in the city of Ahvaz.
The shooting lasted 10 minutes and it came from a park near the parade. Attackers were wearing military uniforms, according to reports.
Gunmen have opened fire during an Iranian military parade in the south-western city of Ahvaz, killing several people, state media says.
The attackers shot from a park near the parade and were wearing military uniforms, reports say.
Pictures from the scene show wounded soldiers being taken to safety.
Iran is marking the anniversary of the beginning of the 1980-88 war with Iraq with several nationwide parades.