The US and Israel are complicit in the deadly shooting at the military parade in the city of Ahvaz that claimed dozens of lives, Hossein Salami, deputy head of Iran's Revolutionary Guards (IRGC), said live on state television.
The Islamic State group also claimed responsibility.
The attack has further shaken Iran, already facing turmoil in the wake of the American withdraw from Tehran's nuclear deal with world powers and additional USA sanctions that are due in November.
Brig-Gen Hossein Salami said in a speech to mourners at Monday's funeral: "You have seen our revenge before. we promise that our response will be crushing and devastating and you will regret what you have done".
Iran has declared today a national day of mourning.
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Isil's official news agency, Amaq, released a video purporting to show three of the four gunmen shortly before the attack.
"We will punish the terrorists, one by one", he promised the crowd.
Militants disguised as soldiers opened fire on an annual Iranian military parade in the southwestern city of Ahvaz. "The United States has not ever supported Daesh, its creation, its frightful attacks in any form, or fashion".
Thousands attended a funeral Monday for members of Iran's elite Revolutionary Guard killed in the assault, leading to chants of "death to Israel", and "death to America". It also has steadily ramped up pressure on Iran to try to get it to stop what Washington calls "malign activities" in the region.
Responding to Rohani's accusations, the USA ambassador to the UN, Nikki Haley, told the BBC that Iran should "look in the mirror" for the causes of the attack, saying that Iran had "oppressed its people for a long time".
Fars and IRNA news agencies said on Monday five attackers were killed, not four as previously reported by state media.
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U.S. Secretary of State Mike Pompeo, asked by a Fox News interviewer if the United States played any role in the attack, said: "When you have a security incident at home, blaming others is an enormous mistake".
Accusations against Gulf countries will nearly certainly antagonise Iran's regional foe Saudi Arabia.
The UAE's foreign minister responded to accusations of involvment in the attack on Twitter, calling them "regrettable and unfounded".
The senior commander of the Islamic Revolution Guards Corps, Brig.
Trump administration policy does not seek a change of government in Iran even though it is reimposing sanctions that are crippling the country's economy after Trump pulled out of the 2015 Iran nuclear agreement.
The statements being made by Iran's leadership, including Supreme Leader Ayatollah Khamenei on Monday, have all reinforced the idea that regardless of which group carried out the attack, the support came from further overseas.
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