The Syrian regime is on the brink of retaking the whole city of Aleppo, which has been partly held by rebels for more than four years.
While CNN sources say eastern parts of the city are still under rebel control, the regime has made extensive gains in the past two weeks.
Up to 9,000 people have already been taken out of the besieged city in nine convoys since Thursday, including 108 wounded, according to Russian and Syrian state media. On Friday, Syrian state television reported that evacuation convoys had been suspended.
Speaking during a trip to Japan, Putin said he had proposed national Syrian peace talks during a phone call to Turkish President Recep Tayyip Erdogan on Thursday.
He suggested they could be held in Kazakhstan.
"Syrian forces have achieved success in allowing the Syrian people to lead their ordinary lives and return to their homes, next step is an agreement about stopping all the fighting, all the shooting," he told reporters.
In the same press conference, Putin blamed ISIS forces' recapture of Palmyra
in the past week on poor cooperation between Syrian, Russian and Western coalition forces.
Assad celebrates 'liberation'
On Thursday, Syrian President Bashar al-Assad celebrated the "liberation" of Aleppo, congratulating the Syrian people and saying "history is being written by every Syrian citizen."
The statement was released on Assad's office's YouTube channel.
US Secretary of State John Kerry described what had already occurred in Aleppo as "unconscionable," adding all sides had to work together on a ceasefire.
"There remains tens of thousands of lives that are now concentrated into a very small area of Aleppo, and the last thing anybody wants to see -- and the world will be watching -- is that that small area turns into another Srebrenica," he said.
Turkish President Erdogan said there were a lot of people left in eastern Aleppo. "I hope the (evacuation) process will not be interrupted," he said, according to Turkish state news agency Anadolu.
On Friday, an activist working inside Aleppo broke down talking to CNN reporters, saying he wasn't sure if his children would ever return to Aleppo.
"We waited for the international community and the United Nations to punish the criminal and not the victims (the people). Unfortunately the punishment was for the people," he said.
"They have displaced us from our land."