Ties between Erdogan and Assad were severed after the outbreak of fighting in Syria in 2011.
“We are in constant contact and our relations are developing,” the Russian leader told Assad at the televised start of their meeting, hailing “significant results in the fight against international terrorism”.
Assad said the visit would mark “a new facet” in his country’s ties with Moscow.
Kremlin spokesman Dmitry Peskov earlier told reporters the talks would focus on bilateral ties but said “Türkiye-Syria relations will certainly be touched upon in one way or another”.
Syria’s war strained relations between Damascus and Ankara, which has long supported militant groups opposed to Assad.
Erdogan has indicated he could meet with Assad, and their defense ministers met in Moscow in December, in the first such talks since the Syrian war began.
Diplomats from Russia, Türkiye, Syria and Iran are due to meet in Moscow this week to pave the way for a foreign ministers’ meeting, according to Turkish media.