Mobile phone footage published by the state-run Islamic Republic News Agency showed members of Iran's IRGC and army forces in dress uniform scrambling to the ground while gunfire erupted around them.
He dismissed a claim by the Islamic State group for the attack.
In this photo provided by Mehr News Agency, civilians try to take shelter in a shooting, during a military parade, marking the 38th anniversary of Iraq's 1980 invasion of Iran, in the southwestern city of Ahvaz, Iran.
Foreign Minister Mohammad Javad Zarif said on twitter that Iran would respond "swiftly and decisively" to the attack, which he blamed on "regional terror sponsors and their USA masters".
"Iran will respond swiftly and decisively in defence of Iranian lives", Zarif wrote on Twitter.
Ahvaz is in the center of Khuzestan province, where there have been sporadic protests by minority Arabs in predominantly Shi'ite Iran.
ISNA said an unnamed spokesman for the elite Revolutionary Guards security force blamed Arab nationalists backed by Saudi Arabia for the attack.
Iran summoned diplomats from Denmark, the Netherlands and Britain to complain about them "hosting some members of the terrorist group" and "double standards in fighting terrorism", the foreign ministry said.
Mr Rouhani said the "bully" USA and the Gulf states it backed had enabled the attack.
Yacoub Hor al-Tostari, a spokesman for the Arab Struggle Movement for the Liberation of Ahvaz, told The Associated Press his group wants that area of southwest Iran to be its own nation.
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According to PTI, another unnamed passenger said that the plane "circled overhead for around half-an-hour before landing". Others posted videos from the cabin, showing passengers sitting quietly and breathing through oxygen masks.
"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.
In the last decade, mass-casualty militant attacks have been incredibly rare.
Russian President Vladimir Putin on Saturday denounced the attack, offering condolences to Iranian President Hassan Rouhani and calling for stronger anti-terrorism cooperation.
Iran was quick to blame Israel and the U.S. for the attack, dismissing Islamic State's (IS) claim that they were behind it. He told an Iranian opposition group that U.S. sanctions on Iran are leading to economic pain that could lead to a "successful revolution".
Speaking before leaving Iran to attend the 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 its annual Country Reports on Terrorism released on September 19, the State Department claimed that Iran remains the world's leading state sponsor of terrorism and is responsible for intensifying multiple conflicts and undermining U.S. interests in Syria, Yemen, Iraq, Bahrain, Afghanistan, and Lebanon.
The incident comes as the Iranian government tries to parry what it sees as a US -led war on its economy after President Donald Trump withdrew from the nuclear deal and reimposed sanctions. Rouhani said the US withdraw from the nuclear deal was an attempt to get Iran to give up its military arsenal.
"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", Shekarchi told state television.
Saturday's attack comes after a coordinated June 7, 2017 Islamic State group assault on parliament and the shrine of Ayatollah Ruhollah Khomeini, the leader of Iran's 1979 Islamic Revolution.
IS's Amaq agency has also claimed it carried out the attack.
"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.