Mr. Bahram Ghasemi offered condolences to the Syrian government and people and also families of Iraqi victims killed and injured during two consecutive attacks which hit the pilgrims.
Two explosions killed more than 40 people in the Syrian capital of Damascus on Saturday in an attack that seemed to target Shiites visiting holy sites from Iraq.
Most of the killed are Iraqi nationals and Iraq's Foreign Ministry spokesman Ahmed Jamal claims all the dead are from their country.
The cemetery is one of the capital's oldest and is where several prominent religious figures are buried.
Syria State TV aired footage from the scene showing blood-soaked streets and several damaged buses in a auto park, apparently where the explosions went off near Bab al-Saghir cemetery.
This is one of the bigger al-Qaeda attacks on civilians over the course of the Syrian Civil War. The area was splattered with blood and shoes were scattered on the ground.
Levant Swords rebel group has reportedly claimed the responsibility of the double bombing attack on buses of Shia pilgrims parked outside the cemetery.
The Damascus attack could provide the impetus for increased Iraqi strikes against IS in Syria, which Baghdad has already carried out near the border. Shiites from across the middle east and Asia often visit shrines in Syria, according to the AP. Iranians and other Shiites from Asia are often also among the pilgrims to the area.
The letter condemned the "cowardly" attack which coincided with a series of mortar and rocket attacks on the city that resulted in a large number of casualties, SANA news agency reported. The Daesh organization claimed that attack.
Also Sunday, two Syrian opposition figures said the Syrian armed opposition will not take part in a meeting planned and sponsored by Russian Federation and Turkey in the Kazakh capital of Astana on Tuesday, saying the government has not been abiding by a cease-fire.