Iran's intelligence ministry reportedly says 22 people have been arrested in connection with Saturday's gun attack on a military parade in Ahvaz.
A statement reported by the semi-official Tasnim news agency also said "weapons, exclusive material and communication equipment were seized".
The ministry blamed a "five-member terrorist group" for the attack.
Iran's president alleged on Sunday the men were armed by a Gulf state allied with the US.
The deputy head of the Revolutionary Guards meanwhile warned the US and Israel to expect a "devastating" response, accusing them of involvement.
But US defence secretary Jim Mattis called Iran's claims of US involvement "ludicrous", and told reporters he was not concerned by the threats.
"We've been very clear that they shouldn't take us on like that," he said. "And I am hopeful that cooler, wiser heads will prevail."
Ethnic Arab separatists and the Islamic State group (IS) have issued competing claims that they carried out the attack, which was the deadliest in Iran in almost a decade.
What happened on Saturday?
The parade in Ahvaz - the capital of the south-western border province of Khuzestan - marked the anniversary of the start of Iran's 1980-88 war with Iraq.
Four gunmen reportedly wearing military uniforms opened fire on troops taking part in the event, bystanders, and a viewing stand for officials.
At least eight of those killed were Revolutionary Guards personnel. Women, children and a disabled war veteran were also among the victims, officials said.
On Monday, thousands of people gathered outside the Sarallah mosque in central Ahvaz for their funerals.
The coffins were draped in Iranian flags and mourners carried pictures of those killed, as well as banners saying "we will stand to the end" and "no to terrorism".
Who was behind the attack?
Speaking at the funeral, Mr Alavi said intelligence ministry agents and other security personnel would catch all of those connected to the attack, adding that a majority were already in custody.
"We will punish every single one of the terrorists for their actions," he vowed.
Iranian officials have said they believed the gunmen had links to an "Ahvazi terrorist group".
A spokesman for the al-Ahwaz National Resistance, an umbrella movement for Arab separatist groups fighting for independence for Khuzestan province, has said it carried out the attack. But one of the separatist groups, the Ahwazi Democratic Popular Front, has denied any involvement.
IS has also claimed the shooting and published a video purportedly showing three of the gunmen being driven to the military parade in a car.
The men appear to be dressed in Revolutionary Guards uniforms and talk about the importance of jihad. However, none of them stated that they were members of IS or pledged allegiance to the group's leader, Abu-Bakr al-Baghdadi - something that is common in such pre-attack videos.
How has Iran threatened to respond?
The deputy head of the Revolutionary Guards accused Saudi Arabia, Israel and the US of masterminding the attack and promised they would face repercussions.
Brig-Gen Hossein Salami said in a speech to mourners at Monday's funeral: "You have seen our revenge before... we promise that our response will be crushing and devastating and you will regret what you have done."
The US permanent representative to the UN, Nikki Haley, said on Sunday that it "condemns any terrorist attack anywhere" and that the Iranian president needed to "look in the mirror" rather than blame her country.
There was no immediate response from the Saudi or Israeli governments.