According to the press service, Assad and Rouhani expressed satisfaction with the level of Syria-Iran relations and agreed to continue coordination of actions at all levels.
"Rouhani stressed that Tehran will continue to provide Syria with everything necessary to complete the fight against terrorism and start rebuilding the country," the press service said in a statement.
"Rouhani informed Assad about the results of the meeting of the guarantor countries in [Russia's Black Sea resort of] Sochi, the sides agreed on achieving the desired progress in order to preserve the territorial integrity of Syria, its independence and sovereignty, and eliminate terrorism throughout its territory," the statement said.
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The SANA news agency also reported that Assad met Iran's Supreme Leader of the Islamic Revolution of Iran Ayatollah Ali Khamenei and congratulated him with the 40th anniversary of the Iranian Islamic revolution.
During the meeting, Khamenei also congratulated Assad on the victories of the Syrian army.
"These victories dealt a decisive blow to the Western and American plans in the region, which calls for even greater caution as to what they can orchestrate in the future as a reaction to their loss," the press service cited Khamenei as saying.
According to the press service, the sides emphasised their intention to continue to resist the policy of escalation carried out by a number of Western countries against Damascus and Tehran, as well a to thwart any attempts to wreak havoc in the region.
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Syria has been in a state of civil war since 2011, with the government forces fighting against numerous opposition groups and militant and terrorist organizations. Russia, along with Turkey and Iran, is a guarantor of the ceasefire regime in Syria. Moscow has also been providing humanitarian aid to residents of the crisis-torn country.