In a televised speech on Monday before the funeral of the victims in Ahvaz, Salami blasted the United States and Israel over the deadly attack.
"You have seen our revenge before… You will see that our response will be crushing and devastating and you will regret what you have done," Hossein Salami said.
Iran's intelligence minister said a "large" network of suspects have been arrested in relation to the attack on the military parade, according to Mizan News Agency.
Iran's Revolutionary Guards reportedly promised "deadly and unforgettable" retaliation against attackers at a military parade in the southwestern Iranian city of Ahvaz on September 23.
On Saturday, armed terrorists opened fire at a military parade, leaving at least 28 people dead and injuring another 60, according to media reports.
Following the incident, Iranian Supreme Leader Ayatollah Ali Khamenei accused the US-backed states of the region of being responsible for the terrorist attack.