He adds: "We will destroy them with a strong and guerrilla-style attack, inshallah (God willing)".
Iranian President Hassan Rouhani also claimed that U.S. backed states in the Persian Gulf were responsible for the assault.
There was no immediate comment from Saudi Arabia on Mr Rouhani's allegations.
The deputy head of Iran's Revolutionary Guards has warned the U.S. and Israel to expect a "devastating" response after accusing them of involvement in an attack on a military parade in the city of Ahvaz.
"A large part of this network has already been arrested", Intelligence Minister Mahmoud Alavi was quoted as saying by the judiciary's news agency Mizan, on the sideline of the funeral of the victims in Ahvaz.
Denmark's ambassador to Iran was on Saturday night called to a meeting with officials in Tehran following a deadly attack on a military parade. "We warn all of those behind the story, we will take revenge", he said.
The ceremony in front of the Sarallah Mosque was attended by thousands of people including soldiers, clerics and officials.
As he spoke the crowd chanted, "Death to America" and "Death to Israel".
Responding to Rohani's accusations, the US ambassador to the UN, Nikki Haley, told the BBC that Iran should "look in the mirror" for the causes of the attack, saying that Iran had "oppressed its people for a long time".
"Based on reports, this cowardly act was the work of those very individuals who are rescued by the Americans whenever they are in trouble in Iraq and Syria and who are funded by the Saudis and the (United) Arab Emirates", he said in remarks posted on his website.
Journalists and onlookers turned to look toward the first shots, then the rows of marchers broke as soldiers and civilians sought cover under sustained gunfire.
The attack was then claimed by another Ahvazi group, the Arab Struggle Movement for the Liberation of Ahwaz, and the Islamic State group also claimed involvement.
The footage, released by the Amaaq news agency, shows three men in a vehicle, apparently on their way to carry out the attack. "We are Muslims, they are kafirs (non-believers)", the man says.
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.
He wrote on Twitter: "Terrorists recruited, trained, armed & paid by a foreign regime have attacked Ahvaz".
In an August 2017 article, Bolton proposed one of the ways the U.S. could pressure Iran would be through supporting ethnic minorities like Kurds, Balochis and the Arabs of Khuzestan - the wider province Ahvaz is capital of.