Assad congratulated Rouhani on winning a second term and for earning "the trust the Iranian people gave him to continue bolstering Iran's position and role," according to a statement carried by Syrian state news agency SANA.
The Syrian president stressed the need to "continue working and cooperating with the Islamic Republic of Iran to strengthen the security and stability of both countries, the region and the world," it said.
Iran, alongside Russia, is a key supporter of Assad, in power for 17 years and engaged in a devastating six-year war against a multitude of rebel and jihadist forces.
Fighters from Iran-backed Lebanese armed Shiite movement Hezbollah and Iraqi Shiite militias are also battling alongside Syrian regime forces.
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According to a report published in March, some 2,100 combatants sent by Iran have died in Syria and Iraq.
Iranian and Russian military support, as well as that of Hezbollah, have helped the Syrian regime win key victories against rebel and jihadist forces.