The Syrian presidency released a handout showing the two leaders meeting.
Putin said that at talks with the Syrian president, they had coordinated joint moves in fight against terrorism in Syria, "emphasizing major results the Syrian army has achieved to this respect, and came to the conclusion that a favorable situation exists at the present moment to bolster a political process".
The latest round of Syria peace talks in the Kazakh capital Astana wrapped up on Tuesday, but did not however make any concrete progress towards ending the seven-year conflict that has cost 350,000 lives.
Assad said the areas controlled by terrorists have substantially diminished.
The Russian president said: "Given the victories and successes of the Syrian army in the war on terror, in light of the onset of a more active period, and in light of the fact that a more active political process has begun, foreign armed forces will start leaving Syrian territory".
It said that Assad confirmed that he would send a list of candidate names as soon as possible to the United Nations for membership in a committee that would discuss the constitution. Putin said Russian Federation welcomes and supports this decision based on agreements reached in national dialogue meetings in Sochi.
The two leaders discussed the need to strengthen the work on rendering of humanitarian aid to Syrians and economistsview Syria.
Russian Federation is a key ally of Assad and has provided support which has allowed the Syrian regime to make territorial gains in recent months against rebels.
Moscow launched an air campaign on behalf of Assad's forces in 2015 that tipped the conflict in his favour.
Assad's future has been a key sticking point in years of failed peace efforts.