"The liberation of Aleppo from radical elements is a very important part of the normalisation in Syria, and I hope, for the region overall," Putin told defence minister Sergei Shoigu in a meeting, the Kremlin said.
The Syrian army said late yesterday that it had retaken full control of Aleppo, scoring its biggest victory against opposition forces since the civil war erupted in 2011.
The Kremlin strongman said that after the ouster of rebels from Aleppo, Moscow will now look to end fighting across the country.
"In any case, we will strive toward this."
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Putin said during his annual press conference today that he hoped that fresh peace talks could get all sides in the conflict to agree to a nationwide ceasefire.
"The next step must be the conclusion of a ceasefire agreement on all of Syria's territory," he said.
Putin said that the presidents of Turkey, Iran and Syria had agreed to take part in new peace talks, which Russia had proposed take place in the Kazakh capital Astana.
Moscow has been conducting a bombing campaign in Syria in support of long-time ally President Bashar al-Assad since September 2015 and has taken steps to boost its presence in the country.
Shoigu said today that some 34,000 people had been evacuated from rebel-held eastern Aleppo since December 15.
The Kremlin said today that Putin had signed an order to expand Russia's naval facility in the Syrian city of Tartus and allow Russian warships into Syrian waters.
Russia's defence ministry said in October that Moscow was poised to transform the Tartus facility into a permanent base, without providing a timeline for its transformation.
Putin that month approved a law ratifying Moscow's deal with Damascus to deploy its forces in the country indefinitely, firming Russia's long-term presence in the country.