A statement reported by the semi-official Tasnim news agency also said "weapons, exclusive material and communication equipment were seized".
Iran's president alleged on Sunday the men were armed by a Gulf state allied with the US.
"We promise that our reaction will be devastating, we warn everyone that we will take revenge", he told mourners. "And I am hopeful that cooler, wiser heads will prevail".
The attack, one of the worst against the most powerful military 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. Khuzestan province also has seen recent protests over Iran's nationwide drought, as well as economic protests.
Describing the attack on defenseless people as an act of cowardice, the Leader noted, "According to [available] reports, this cowardly act has been perpetrated by the same people who are saved by Americans whenever they face a hard situation in Iraq and Syria" and whose operations are being financed by Saudi Arabia and the United Arab Emirates.
Among those being mourned was a disabled war veteran and a four-year-old boy, as well as at least 12 members of Iran's elite Revolutionary Guard.
Pictures of women and children scrambling to find cover evoked an emotional response from Iranians.
On Monday, thousands of people gathered outside the Sarallah mosque in central Ahvaz for their funerals.
Who was behind the attack?
Iran's elite Guards vow to avenge deadly attack
President Donald Trump, left, on July 22, 2018, and Iranian President Hassan Rouhani on February 6, 2018. Armed men conducted the attack in the southwestern city of Ahvaz, according to Iranian state television.
Many had already been arrested in connection with the attack, according to Mizan news agency.
"We stand with the Iranian people against the scourge of radical Islamic terrorism and express our sympathy to them at this awful time", Nauert said.
Iranian officials blamed Arab separatists, backed by Gulf Arab allies of the United States, for the operation.
The region's Arab separatists, once only known for nighttime attacks on unguarded oil pipelines, claimed responsibility.
The attack on the military parade is likely to give security hardliners like the Guards more political ammunition because they did not endorse the pragmatist Rouhani's pursuit of the nuclear deal with the West, analysts say.
Iranian soldiers used their bodies at times to shield civilians in the melee, with one Guardsman in full dress uniform and sash carrying away a bloodied boy.
IS had claimed the attack via its propaganda mouthpiece Amaq, and that the attack was in response to Iranian involvement in conflicts across the region.
How has Iran threatened to respond?
Iranian leaders accused the United States of complicity in the attacks in Ahvaz.
Guards Brigadier General Hossein Salami, in a speech broadcast on state TV, said: "You have seen our revenge before". The shooting was the deadliest terror attack to strike the country in almost a decade.