Tehran "congratulates the victory of the Syrian army and people over the 'takfiri' terrorists," Abdollahian said, using a term for Sunni militants who comprise the majority of the country's rebels.
Iran is a predominantly Shiite Muslim country, and a close ally of Assad, who belongs to the Alawite sect, an offshoot of Shiite Islam.
"Certain parties continue to send arms and support terrorist actions in Syria," Abdollahian added, saying they "are responsible for massacres and destruction in Syria and should be tried for war crimes."
Earlier today, the army and allied fighters from the Lebanese Shiite movement Hezbollah seized control of Qusayr after an 18-day battle.
Iran is Syria's key ally in the Middle East.