Many held pictures of a four year old boy killed in the attack, one of the worst against the most powerful military force of the Islamic Republic.
Four assailants were reported to have been involved in the Ahvaz assault and all were killed as Iranian troops returned fire during the attack and in the subsequent pursuit.
The "formal incitement against the UAE from within Iran is unfortunate, and has escalated after the Ahvaz attack", said Minister of State for Foreign Affairs Dr Anwar Mohammed Gargash in a tweet.
"Iran's answer (to this attack) is forthcoming within the framework of law and our national interests", said Mr Rouhani, adding that the USA would regret its "aggressiveness". "You will see that our response will be crushing and devastating and you will regret what you have done", Hossein Salami said in a speech broadcast live on Iran state television.
Three Arab activists said that security forces, especially the intelligence branch of the Revolutionary Guards, had detained more activists in Ahvaz.
"It is unacceptable that these groups are not considered to be terrorist groups by the European Union provided they do not commit acts of terror in Europe", Iranian foreign ministry spokesperson Bahram Qasemi said.
Speaking before leaving Teheran to attend the annual UN General Assembly in New York, Mr Rouhani accused US-backed Gulf Arab states of providing financial and military support for anti-government ethnic Arab groups in Iran.
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General Hossein Salami, acting commander of the Revolutionary Guard vowed revenge on the perpetrators of the attack and what he called the "triangle" - or Saudi Arabia, Israel and the United States - saying operatives would be harshly punished.
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.
Ahvaz National Resistance, an Iranian ethnic Arab opposition movement which seeks a separate state in oil-rich Khuzestan province, also claimed responsibility.
Iranian officials have said they believed the gunmen had links to an "Ahvazi terrorist group". But it is unlikely the IRGC will strike any of these foes directly.
In New York, Trump's personal lawyer Rudy Giuliani said on Saturday that U.S. sanctions were inflicting economic pain on Iran that could lead to a "successful revolution".
On June 7, 2017 in Tehran, 17 people were killed and dozens wounded in simultaneous attacks on the parliament and on the tomb of revolutionary leader Ayatollah Ruhollah Khomeini - the first inside Iran claimed by IS.
He wrote on Twitter: "Terrorists recruited, trained, armed & paid by a foreign regime have attacked Ahvaz. It is Americans who instigate them and provide them with necessary means to commit these crimes", Rouhani said before leaving for the U.N. General Assembly in NY.
The accusation will nearly certainly antagonize Iran's regional foe Saudi Arabia.