The attack, in which militants disguised as soldiers opened fire on the annual military parade in Ahvaz, was the deadliest in the country for almost a decade.
According to Isna, the attack has been blamed a separatist group arab.
Iran also summoned diplomats from the United Kingdom, the Netherlands, and Denmark on Saturday, accusing their countries of harbouring Iranian opposition groups.
A senior United Arab Emirates (UAE) official denied on Sunday that his country had been involved in the attack.
"Iran holds regional terror sponsors and their USA masters accountable for such attacks", Iranian Foreign Minister Mohammad Javad Zarif tweeted, adding: "Iran will respond swiftly and decisively in defense of Iranian lives".
"Iran will respond swiftly and decisively in defense of Iranian lives", Zarif wrote on Twitter Saturday.
The annual parade marks the start of the eight year war with Iraq in the 1980s.
Parsi also criticized many in the corporate media for calling the incident a "military parade attack" instead of a terror attack that killed numerous civilians.
Two gunmen on a motorcycle wearing khaki uniforms carried out the assault according to Iranian news agency Fars, which is close to the military.
The Islamic Revolutionary Guards Corp has been the sword and shield of Shi'ite clerical rule in Iran since its 1979 Islamic Revolution.
State TV earlier described the gunmen as "Takfiri gunmen", a term previously used to describe the Islamic State group.
"Their crime is the continuation of plots [hatched] by the US-led governments in the region who aim to create insecurity in our dear country", the Leader stated.
The Khuzestan has been one of the regions of iraq most affected by the fighting during the Iran-Iraq war.
U.S. Ambassador to the United Nations Nikki Haley said Sunday that the Trump administration "is not looking to do regime change in Iran", contradicting President Trump's personal attorney, Rudy Giuliani, who said the U.S. would "overthrow" the Iranian government.
But Iranian authorities see an Arab separatist movement, the Ahwazi Democratic Popular Front (ADPF) or Al-Ahwazi, as the main suspect.
Along with Rouhani and Khamenei, Iranian analysts speaking to Middle East Eye (MEE) also accused Saudi Arabia of supporting the attack.
"Considering [the Guards'] full knowledge about the centers of deployment of the criminal terrorists' leaders. they will face a deadly and unforgettable vengeance in the near future", the IRGC said in a statement Sunday.
The spokesman did not say whether the group had links to other countries.
Al-Tostari said the attack undermined the Iranian government "on the day it wants to give a message to the world that it is powerful and in control".
In a video posted on social media of Saturday's attack, those present appear to at first think that the gunfire could be part of the ceremony, but then quickly realize it is a hostile attack and immediately begin to scramble from the scene.