Seyed Abbas Mousavi voiced Iran’s sympathy with the families of the martyrs, prayed God to elevate their ranks in Heaven and wished quick recovery for the injured.
On Tuesday a walkway collapsed and set off a mass stampede in Karbala as hundreds of thousands of Shia Muslims marked Ashura.
At least 31 people were killed and about 100 were injured, officials said on Tuesday. At least 10 among the wounded pilgrims were in a critical condition, according to the Iraqi health ministry.
No Iranian pilrgims were reprotedly among those who lost their lives in the incident.
It was the deadliest stampede in recent history during Ashura commemorations, when hundreds of thousands of people converge on the city, about 80km south of Baghdad, every year to mourn the martyrdom anniversary of Imam Hussein (AS) and his companions in the 680 Battle of Karbala.
The deadly rush began when part of a walkway collapsed during a procession, causing mass panic among worshippers.
Millions of people in Iran, Pakistan, Afghanistan, India, Bangladesh, and Lebanon also marked the day with mourning ceremonies.