The Kremlin said in a statement on Wednesday that "The situation in Syria has been discussed".
Assad travelled to Moscow for his first known foreign trip since the conflict broke out in his country in 2011, holding landmark talks on the future of Syria with Putin.
Russian Foreign Minister Sergei Lavrov also held phone talks with US Secretary of State John Kerry, with the two agreeing to meet for talks on Syria in Vienna on Friday.
Foreign ministers from Turkey and Saudi Arabia - which have been among the most vocal opponents of the Assad regime - are also set to take part in the Vienna talks.
Putin has been seeking to muscle his way back onto the world stage after months of Western isolation over the Ukraine crisis. On September 30, he launched a bombing campaign in Syria.
Saudi Foreign Minister Adel al-Jubeir said last month that Assad must leave office or face being turfed out by force.
Putin met Saudi Arabia's Defence Minister Prince Mohammed bin Salman earlier this month for talks about the possibility of a political solution in Syria.
Moscow also proposed another meeting to be held on Friday, of the "Quartet" of Middle East peace mediators - Russia, the US, the European Union and United Nations - given the "extremely tense situation" in the Middle East.
Source: Reuters And AP