"It is absolutely clear to us who has done this, which group it is and to whom they are affiliated", Rouhani said on state television ahead of his departure from Tehran for this week's U.N. General Assembly in NY.
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.
The Revolutionary Guards are the most powerful and heavily armed military force in the Islamic Republic and also have a vast stake worth billions of dollars in the economy.
However Iran has previously accused its regional rival, Saudi Arabia, of supporting separatist activity amongst Iran's Arab minority.
Iran's leaders have blamed the attack on the United States.
Israel is also a key United States ally opposed to Tehran.
"The response of the Islamic Republic of Iran to the smallest threat will be crushing", Mr Rouhani said on his official website.
Rouhani's comments blaming the U.S. came as Iran's Foreign Ministry summoned diplomats from Britain, Denmark and the Netherlands over them allegedly providing havens for the separatists.
"Based on its policy on using terrorism as a means...the U.S. is responsible for the durability of the ominous phenomenon of terrorism in the world, particularly in the Middle East, and it should be held accountable for violent behavior and measures by these groups", Iranian Foreign Ministry Spokesman Bahram Qassemi said on Sunday.
The Islamic State (IS) jihadist group has claimed responsibility for the rare assault, which saw gunmen spray a crowd with gunfire in the southwestern city of Ahvaz on Saturday. He did not identify the attackers. The group provided no evidence for the claim.
The al-Ahvazieh militant group claimed responsibility for the attack on the parade on Saturday in the city of Ahvaz, in which at least 25 people were killed and 60 others injured, including children, IRNA said.
"The ambassadors of the two countries declared that their governments were ready to share any information with regards to the terrorists and their records".
"It is expected that (the Danish and Dutch) governments hand over the perpetrators of this attack and anyone related to them to Iran for a fair trial", he added.
The state-run IRNA news agency reported that the wounded included a woman and a child but did not elaborate.
Iran has been relatively stable compared with neighbouring Arab countries that have grappled with upheaval since the 2011 uprisings across the Middle East.
"Several gunmen began shooting from behind the stand during the parade".
One of the victims was a four-year-old girl.
However, Emirati academic Abdulkhaleq Abdulla, has tweeted on the Ahwaz attack by saying: "A military attack against a military target is not a terror act".
TRT World spoke to political analyst Mohammad Marandi about the attack.
Of those killed, at least eight are believed to be members of Iran's elite Revolutionary Guard.
Oil-rich Khuzestan in the past has seen attacks oil pipelines by Arab separatists.