The crowd also chanted slogans of "Death to U.S." and "Death to Israel" - chants staple at Iranian political rallies.
AFP reporters saw members of the public and the military carrying coffins draped in the Iranian flag, some bearing pictures of the deceased.
The annual parade marks the start of the eight year war with Iraq in the 1980s.
Journalists and onlookers turned to look toward the first shots, then the rows of marchers broke as soldiers and civilians sought cover under sustained gunfire. One soldier picked up a gun and got to his feet as women and children fled for their lives.
Iran's Foreign Minister, Mohammad Javad Zarif, has blamed regional countries and their "US masters" for the attack.
But in a statement on its website, the group denied any involvement, accusing Iranian authorities of ordering the attack to distract from Tehran's support for "militias in the region".
The bloodshed struck a blow to security in OPEC oil producer Iran, which has been relatively stable compared with neighboring Arab countries that have grappled with upheaval since the 2011 uprisings across the Middle East.
Earlier in the day, Iran's intelligence minister Mahmoud Alavi told the media the security services uncovered a large network of suspects. He did not elaborate.
Ethnic Arab separatists and the Islamic State group (IS) have issued competing claims that they carried out the attack, which was the deadliest in Iran in nearly a decade.
The men appear to be dressed in Revolutionary Guards uniforms and talk about the importance of jihad.
"We are Muslims, they are kafirs (non-believers)", the man reportedly could be heard saying. He adds: "We will destroy them with a strong and guerrilla-style attack, inshallah (God willing)".
The Islamic Revolutionary Guards Corp (IRGC) has been the sword and shield of Shi'ite clerical rule in Iran since its 1979 Islamic Revolution.
"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.
President Hassan Rouhani vowed on Saturday 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.
A spokesman for the al-Ahwaz National Resistance, an umbrella movement for Arab separatist groups fighting for independence for Khuzestan province, has said it carried out the attack.
"Most of the martyrs were from the Guards", said Ali Hossein Hossein Zadeh, deputy to the Khuzestan provincial governor, referring to the Islamic Revolution Guards Corps, or IRGC. But it is unlikely that they will strike any of these foes directly.
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.