Ali Shamkhani, secretary of the Supreme National Security Council, sent a message to Assad to congratulate him on Sunday's "admirable and honourable" win over the Islamic State group.
Iran's government and its armed forces "will continue to provide Syria with their full support" against the jihadists, Shamkhani said, according to the official news agency IRNA.
Iran provides financial and military support to Assad through its elite Revolutionary Guards, notably sending "military advisers" and "volunteers" to fight alongside the Syrian army.
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Guards chief Major General Mohammad Ali Jafari said "the situation in Syria is very good" after the recapture of Palmyra, Fars news agency reported.
Foreign ministry spokesman Hossein Jaber Ansari also lauded Syria's victory and said that Tehran will continue to back the Assad regime and other governments battling extremism.
"Iran's support continues for the fight against terrorism in Syria, Iraq and countries exposed to this threat," Ansari told Iran's Arabic-language Al-Alam television.
"Syria will march forward strongly in the fight against terrorism and the terrorists definitely won't have a place in the future of the region," he added.
Syrian troops ousted the jihadists from the ancient city on Sunday almost a year after they had seized it.