Saturday's assault, one of the worst ever against the elite force of the Islamic Republic, struck a blow at its security establishment at a time when the United States and its Gulf allies are working to isolate Tehran.
State-run PressTV said the action was taken over comments by an unnamed UAE official, without giving details.
Tehran has, meanwhile, openly blamed the United States and its allies in the Middle East for backing the attackers. The Islamic State group also claimed the attack, but initially offered incorrect information about it and provided no proof. All four attackers were killed.
The parade in Ahvaz, a city with a population of more than a million people, was one of many happening nationwide in honor of Sacred Defense Week, marking the 38th anniversary of Iran's 8-year war with Iraq.
"We are not waiting until there becomes a battle in Saudi Arabia, so we will work so that it becomes a battle for them in Iran and not in Saudi Arabia".
Women and children died in the assault, state news IRNA agency reported.
"Of the four terrorists, three were sent to hell at the scene, while the fourth who had been wounded and arrested went to hell moments ago due to his severe wounds", Mr Shekarchi told state television. Iran holds regional terror sponsors and their United States masters accountable for such attacks.
Iran summoned diplomats from Britain, Denmark and the Netherlands early Sunday for allegedly harboring "members of the terrorist group" that launched the attack. Some members of the ethnic separatist movements are based in the European countries. Moreover, these monarchies are no longer limiting themselves to pushing the U.S. to take military action, but are announcing their own readiness to attack Iran.
Rouhani did not identify those behind Saturday's attack, which was claimed by an Arab separatist group.
- July 20, 2018: at least 10 Revolutionary Guards are killed in an attack led by insurgents against a base in the village of Dari, in the Marivan district of Iran's northwestern Kurdistan region.
The Guards have a big say in Iran's regional interests and a vast stake worth billions of dollars in Iran's economy.
A video distributed to Iranian media showed soldiers crawling to escape gunfire.
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As one of our loyal readers, we ask you to be our partner. "We will respond to these crimes and all the perpetrators will be punished", the president pointed out.
Ahvaz is in the centre of Khuzestan province, where there have been sporadic protests by minority Arabs.
There has been no direct evidence linking the separatists to Saudi Arabia. "With the grace of God, we will pass the difficulties we have been facing over the past months and will make the USA regret, because they [the U.S.] have chosen a wrong path", he said before departure to NY to attend the annual UN General Assembly meeting.
"The Persian Gulf states are providing monetary, military and political support for these groups", said Mr Rouhani.
Zarif said that children and journalists were casualties in the attack.
"They are not from Daesh (Islamic State) or other groups fighting (Iran's) Islamic system. but they are linked to America and (Israel's intelligence agency) Mossad".
"The summoning was over offensive remarks of a (UAE) political advisor", he said in a statement.
Senior Guards commanders have said the Ahvaz attack was carried out by militants trained by Gulf states and Israel and backed by America.
Mr Rouhani is on a collision course with Donald Trump, whose decision to quit the 2015 nuclear deal is, to Mr Rouhani's mind, directly to blame for Iran's financial crisis.
Gunmen attacked a military parade in the Iranian city of Ahvaz on Saturday, killing at least 25 people and wounding 60 others.
Egypt, a key ally of Saudi Arabia, also condemned the attack.
- July 15, 2010: Twin suicide bombings in a crowded Shiite mosque in Zahedan, capital of Sistan-Baluchistan, kill at least 28 people and wound more than 250.