The two leaders met at a gathering location of Russian forces in Syria's capital Damascus, SANA said.
The two leaders were briefed by the head of the Russian forces in Syria on the situation in the country, according to the report.
Putin congratulated the Russian soldiers on the Christmas occasion while Assad expressed appreciation for the deployment of the Russian forces.
During their meeting, Putin told Assad that a stride has been made in regaining the structure of the Syrian state and the territorial integrity of Syria, according to Kremlin spokesman Dmitry Peskov in a statement.
Putin observed the return of normal life to the streets of Damascus, Peskov added.
This is Putin's first visit to Damascus since the Syrian war broke out in 2013 and the second to the Arab country.
In December 2017, Putin visited Russia-operated Hmeimim Air Base in Syria's northwestern province of Latakia, where he met Assad and ordered a partial withdrawal of Russian forces.
Bouthaina Shaaban, an advisor of President Bashar al-Assad, told pan-Arab al-Mayadeen TV that the visit held a lot of connotations including celebrating the return of peace to Damascus.
She went on saying that both leaders were on the same page regarding the need to eliminate terrorism in Idlib province, the last major rebel stronghold in Syria.
The visit of Putin comes as the Syrian army and Russian warplanes have been pounding rebel positions in Idlib for a few weeks.