It remains unclear what the withdrawal would mean for the outcome of the Syrian war or for Assad's future.
Putin and U.S. President Barack Obama spoke by telephone on Monday about Syria, with the Kremlin saying the two leaders "called for an intensification of the process for a political settlement" to the conflict.
11:32 Putin hopes for better ties with U.S., anti-terror action11
10:56 Putin praises Russian unity, calls for better ties with United States11
02:36 Syria blames Turkey for loss of soldiers; government troops advance in Aleppo11
20:14 Syria government forces 'retake largest Aleppo rebel district'18