Ali Reza Rashidian said they will be sent to the Arab country by March 16.
The next round of registration for pilgrimage during Norows holidays (late March) will begin on February 19, he said.
Rashidian noted that sending Iranian pilgrims to the holy sites in Syria resumed nearly a month ago and so far some 500 Iranians have made the spiritual trip.
The holy shrine of Hazrat Zaynab (SA) in Damascus is the most important religious site for Shia pilgrims who visit Syria.
Religious tours to the country had been suspended years ago due to security concerns.