"It is Americans who provide them with their required necessities to perpetrate such crimes", Rouhani said in remarks published on his official website. Women and children scattered along with once-marching Revolutionary Guard soldiers as heavy gunfire rang out, the chaos captured live on state television. The militants have made a string of false claims in the wake of major defeats in Iraq and Syria.
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, which left at least 29 people dead. "The attack will strengthen the IRGC's position inside Iran and in the region", Tehran-based political analyst Hamid Farahvashian said.
Foreign Minister Mohammad Javad Zarif said Iran will respond "swiftly and decisively" to the attack, holding agents of a foreign regime responsible.
Tehran has made no secret of its mounting fury at the U.S. over tightening sanctions, with Javad Zarif, the foreign minister, taking to Twitter on Friday to denounce "the Trump administration's sense of entitlement to destabilise the world along with rogue accomplices in our region".
Iran was holding similar parades in several cities including the capital Tehran and the port of Bandar Abbas on the Gulf.
The semi-official Fars news agency said two gunmen opened fire on the large crowd of spectators and then attempted to attack the viewing stand for official dignitaries before being shot and wounded by security forces. It said gunmen were dressed in Guard uniforms and targeted a riser where military and police commanders were sitting.
That event was held on the day of the deadly attack in Ahvaz.
"Their crime is a continuation of the conspiracies by the USA -backed regimes in the region which have aimed at creating insecurity in our dear country", Khamenei said in a statement.
Meanwhile, relations between the US and Iran continue to spiral downwards following US President Donald Trump's withdrawal from the historic nuclear deal struck between Iran, China, France, the United Kingdom, the US and Germany.
Brigadier General Abolfazl Shekarchi was quoted by IRNA as saying the terrorists were "not from Da'esh (ISIS) or other groups fighting (Iran's) Islamic system ... but are linked to America and the [Israeli worldwide intelligence agency] Mossad".
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 war against the Islamic Republic.
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Afterwards, he was carted off the field, and NFL Network's Ian Rapoport reported the Niners feared it was a torn ACL. Shanahan acknowledged a quarterback move is likely, though Beathard is line to start next week in Los Angeles.
But from early on, Iranian officials saw an Arab separatist movement, the Ahwazi Democratic Popular Front (ADPF) or Al-Ahwazi, as the main suspect.
In 2015, under then-president Barack Obama, the USA and Iran reached a landmark nuclear deal - also signed by China, Russia, the UK, France and Germany - where Iran limited its nuclear activities in exchange for sanctions relief.
Shia Iran has always been locked in a struggle for regional dominance with USA -allied, majority Sunni, Saudi Arabia.
The U.N. ambassador, without mentioning Giuliani, told CNN, "The United States is not looking to do regime change in Iran".
Mr Trump is chairing a UN Security Council meeting on Wednesday - and says the meeting will be focused on Iran.
Both Daesh and an anti-government Arab group called the Ahvaz National Resistance, claimed responsibility for Saturday's attack.
The Iranian elite force, in a statement on Sunday, said that those behind Saturday's attack will face a "deadly and unforgiving revenge in the near future".
The Islamic Revolutionary Guards Corp (IRGC) has been the sword and shield of Shi'ite clerical rule in Iran since its 1979 Islamic Revolution. At least 18 people were killed and more than 50 wounded.
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. "Many people are scared".
Gambrell reported from in Dubai, United Arab Emirates.