Iranian President Hassan Rouhani had vowed a "crushing" response to last month's assault -- claimed by the Islamic State jihadist group -- on a military parade commemorating the 1980-1988 Iran-Iraq war.
"The headquarters of those responsible for the terrorist crime in Ahvaz was attacked a few minutes ago east of the Euphrates by several ballistic missiles fired by the aerospace branch of the Revolutionary Guards," the Guards said on their website.
"Based on preliminary reports, many takfiri terrorists and the leaders responsible for the terrorist crime in Ahvaz have been killed or wounded in this missile attack," they added. The term "takfiri" refers to Sunni Muslim extremists.
The Guards released pictures of what appeared to be missiles lighting up the night sky, leaving trails of smoke as they soared above a desert region with a rugged mountain in the background.
Iran's Fars news agency said the Guards fired "a number of medium-range" Zolfaghar and Qiam missiles, with a range of 750 kilometres and 800 kilometres (465 and 500 miles), respectively.
The agency said the missiles hit the Syrian desert border town of Albu Kamal on the west of the Euphrates River, in the eastern province of Deir Ezzor.
"On at least one of the missiles was written 'death to America', 'death to Israel' and 'death to Al Saud'," it said, a reference to the ruling family in Saudi Arabia, Iran's regional rival.
According to the Syrian Observatory for Human Rights, a Britain-based war monitor, "heavy explosions took place at dawn (Monday) in the last pocket under IS control near Albu Kamal".
Albu Kamal itself, located on the border with Iraq, is held by regime forces and allied regional militiamen who seized it from IS in 2007.
- 'Jihadist separatists' -
Twenty-four people were shot dead in the attack by five gunmen on a military parade in the mainly ethnic Arab city of Ahvaz in southwestern Iran on September 22.
Ahvaz is the provincial capital of Khuzestan, a border region which was a major battleground of the 1980-1988 Iran-Iraq war, and which also saw ethnic unrest in 2005 and 2011.
Iranian officials initially blamed Arab separatists backed by Gulf Arab allies of the United States for the attack.
But on Monday supreme leader Ayatollah Ali Khamenei appeared to link the perpetrators to jihadists operating in Iraq and Syria, where IS once had major strongholds.
"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," Khamenei was quoted by his official website as saying.
The next day Iran's intelligence ministry published photos of five men it said carried out the Ahvaz assault, identifying them as "jihadist separatists".
IS, a Sunni Muslim extremist group which Iran and its Damascus allies are fighting in Syria, has claimed responsibility for the attack and said all five assailants were Iranian, including four from Ahvaz.
It also threatened to carry out new attacks in Iran.
IS had already claimed responsibility for twin attacks in June 2017 on the parliament and the tomb of revolutionary leader Ayatollah Ruhollah Khomeini in Tehran that killed 17 people.
After that assault the Guards said they had fired missiles into Syria that had successfully hit IS targets.