Armed forces spokesman Brigadier General Abolfazl Shekarchi said three of the terrorists involved in yesterday's attacks were shot dead at the scene while a fourth was arrested and later died from his injuries.
Rouhani's comments blaming the USA came as Iran's Foreign Ministry summoned diplomats from Britain, Denmark and the Netherlands over them allegedly providing havens for the separatists.
"The formal incitement against the UAE from within Iran is unfortunate, and has escalated after the Ahvaz attack", UAE's Minister of State for Foreign Affairs Anwar Gargash said in a tweet.
The attack is meant to undermine Iran's security and stability and as "punishment for ... its rejection of American dependency politics", the statement said.
Speaking on Sunday, Rouhani said: "America wants to cause chaos and unrest in our country so that it can return to this country, but these are unreal fantasies and they will never achieve their goals".
Ahvaz National Resistance, an Iranian ethnic Arab opposition movement which seeks a separate state in oil-rich Khuzestan province, claimed responsibility for the attack.
The al-Ahvaziya terror group, whose recruits are believed to be scattered in several European countries, including in the Netherlands and Denmark, claimed responsibility for the attack in Ahvaz.
Iranian Foreign Minister Mohammad Javad Zarif blamed regional countries and their "U.S. masters" for funding and arming the separatists, issuing a stark warning as regional tensions remain high in the wake of the USA withdraw from the Iranian nuclear deal. The attack in Ahvaz, which saw women and children flee with uniformed soldiers bloodied, has further shaken the country.
The terror outfit, which is backed by Saudi Arabia, has a record of carrying out sabotage acts in Khuzestan province, which encompasses Ahvaz and some other towns with Arab population. Rouhani said the USA withdraw from the nuclear deal was an attempt to get Iran to give up its military arsenal.
More generally, the U.S. is deeply suspicious of Iranian activity in the Middle East - including its influence in Syria and Yemen - and is an ally of Israel and Saudi Arabia, two of Iran's opponents.
Trump will fail in his confrontation with Iran, just like Iraq's Saddam Hussein, Iranian President Hassan Rouhani said, referring to the war in the 1980s between the two Middle Eastern powers and vowing that Tehran will not abandon its missiles.
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Senior commanders of the Islamic Revolutionary Guards Corps (IRGC) have said the Ahvaz attack was carried out by militants trained by Gulf states and Israel and backed by America.
He warned the United States will regret its "aggressiveness".
"It is not acceptable that the European Union does not blacklist members of these terrorist groups as long as they do not perpetrate a crime on".
Arab separatists groups have operated in the region for years, according to the New York Times.
Supreme Leader Ayatollah Ali Khamenei described the attack as exposing "the atrocity and viciousness of the enemies of the Iranian nation".
"This crime is the extension of the plots by the USA allies in the region, seeking to create insecurity in Iran", Iran's Supreme Leader Ayatollah Ali Khamenei said in a statement.
A spokesman for an Arab separatist group in Iran says members of his organization carried out an attack on an Iranian military parade that killed 25 people and wounded 53.
Tensions between mainly Shi'ite Iran and mostly Sunni Saudi Arabia have surged in recent years, with the two countries supporting opposite sides in wars in Syria and Yemen and rival political parties in Iraq and Lebanon.
Saudi Arabia hasn't responded to the allegations.
Civilians, including women and children, were among those killed, while at least 53 people have been transferred to local hospitals, according to the source. There have also been economic protests in the region and protests over Iran's nationwide drought.
The United States was not the only country to delay its messages of condolences to Iran - notably, unlike many other nations, it does not have an ambassador in Tehran.