Military forces and citizens who had gathered to watch the parade were among the killed, the report said.
Iran's President Hassan Rouhani vowed earlier Saturday to boost his country'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.
Zarif vowed Iran would "respond swiftly and decisively in defence of Iranian lives".
"Terrorists recruited, trained, armed & paid by a foreign regime have attacked Ahvaz".
In local media, officials began to say that a regional group of Sunni Arab separatists which Iran claims is funded by Saudi Arabia and which has bombed targets in the province in the past were responsible for the attack.
Speaking at a military rally in Tehran, he said Trump will fail in the "economic and psychological war" he's launched against Iran, just as Hussein failed in his eight-year war against the Islamic Republic.
Tehran also summoned diplomats from Denmark, the Netherlands and Britain for allegedly hosting members of the group suspected of links to Saturday's attack near the Iraqi border that left at least 29 people dead.
Iranian President Hassan Rouhani said on Sunday the United States wants to create insecurity in Iran.
Ahvaz is in the centre of Khuzestan province, where there have been sporadic protests by minority Arabs.
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Iran's Foreign Ministry also signaled that the individuals behind the Ahvaz shooting may have had ties to some European countries.
In the last decade, such attacks have been incredibly rare.
State media called the attackers terrorists and reported that all four gunman were killed.
"On behalf of #PADMAZ organization we reject all accusations and we insist that PADMAZ organization is a civil political movement and has nothing to do with what happen today in #IranMilitaryParade attack", the group said on unconfirmed Twitter and Facebook accounts.
This came hours after Iran's Foreign Minister Javad Zarif blamed a "foreign regime" for the attack.
There has been no claim of responsibility for the attack in the city of Ahvaz.
The attack in Ahvaz took place on the eve of President Rohani scheduled departure for NY to attend the United Nations General Assembly. Iran backs militant groups across the region.
A Revolutionary Guard member carries a wounded boy after the attack by unknown militants.
In a keynote speech, Rouhani vowed to boost Iran's ballistic missile capabilities despite Western concerns that were cited by his United States counterpart Donald Trump in May when he abandoned a landmark nuclear deal with Tehran.
He added, "the USA and the occupying regime of Israel are those who train and finance terrorists; those regimes who are our Persian Gulf neighbors train terrorists, and the Islamic Republic of Iran itself is also the victim of terrorism today".
The Islamic State group carried out a coordinated assault in June 2017 on parliament and the shrine of Ayatollah Ruhollah Khomeini, the leader of Iran's 1979 Islamic Revolution.