Responding to a message of congratulations from Assad for his election, Rowhani "expressed certainty that with the efforts of benevolent and peaceful forces, the great and resistant nation of Syria will be able to completely pass the current situation," ISNA news agency reported.
Iran is a staunch supporter of the Assad government in its fight against rebels, whom Tehran regards as "terrorists" backed by Western and Arab countries.
The Islamic republic is in turn accused of arming Syrian government forces in the conflict, which is estimated to have killed more than 100,000 people since it erupted 28 months ago.
In a separate message to Hezbollah chief Hassan Nasrallah, Rowhani said Iran backed the Palestinians and the "Lebanese nation," while highlighting the Shiite militant group's "endeavours" for the anti-Israeli resistant front -- comprised of Iran, Syria and Lebanon.
Rowhani has said one of his foreign policy priorities is to mend difficult relations between Shiite Iran and Sunni-dominated Gulf Arab states, which have been further strained by the Syrian conflict.