A transcript of Thursday's meeting released by the Kremlin quoted Assad as saying that Syria is making progress in fighting "terrorism," which "opens the door to the political process."
Putin's spokesman Dmitry Peskov said Assad informed the Russian leader of his decision to "send a delegation to the U.N." to discuss reforming the country's constitution. The U.N. has hosted several rounds of peace talks in Geneva that have made no progress toward ending the conflict.
A posting on the Syrian presidency's Facebook page said the two leaders consulted on various issues of mutual interest and the latest political and military developments in Syria.
It said Assad confirmed he will send a list of candidate names as soon as possible to the United Nations, for membership in a committee that would discuss the constitution. It said that Russia welcomes and supports this decision based on agreements reached in national dialogue meetings in Sochi.
It said the two also discussed economic cooperation and growing investments by Russian companies in Syria.
Russia has been a key ally of Assad throughout the seven-year Syrian civil war. Moscow launched an air campaign on behalf of Assad's forces in 2015 that tipped the conflict in his favor.
Assad previously visited Russia and met with Putin in November 2017 and October 2015, and Putin traveled to the Russian air base in Syria last December to announce a scale-back of the Russian military presence there.
Russian state television on Thursday aired footage of the two leaders meeting. Putin told Assad that "a lot has been done" at Russia-sponsored talks between the Syrian government and the opposition in Kazakhstan.
"Now we can take the next steps together with you," Putin told Assad.
Assad said he is committed to political reform, without elaborating.
Syria's conflict began with mass protests against the Assad family's decades-long rule. A brutal government crackdown and the rise of an armed insurgency eventually tipped the country into civil war. More than 450,000 people have been killed and 11 million have been displaced from their homes.
Assad's future has been a key sticking point in years of failed peace efforts. The opposition and its Western backers have demanded he step aside as part of a political transition, something the Syrian government has adamantly rejected.
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