Erdogan informed Putin of the strike that killed four Turkish soldiers, presidential sources said, which the Turkish army assessed to have been by the forces of President Bashar al-Assad early on Thursday.
It was the first time Turkey had blamed the Assad regime -- which is given military support by Russia -- for a deadly strike on its troops during Ankara's three month campaign inside Syria.
Erdogan and Putin also agreed to accelerate their efforts to find a solution to the humanitarian crisis in Aleppo, where the regime continues its Moscow-backed offensive to recapture the whole city, which is divided between the government and rebels.
During the phone call, Erdogan told Putin of how the Turkish-backed offensive in Syria was evidence of Ankara's determination to fight against terror, the sources added.
The president stressed Turkey's commitment to Syria's territorial integrity -- Russia had previously said it was "deeply concerned" by Turkey's incursion while Damascus has called it a "blatant violation of sovereignty".
The presidents also backed the process to normalise relations between Russia and Turkey after the crisis sparked by the shooting down by Turkish forces of a Russian jet over Syria last year.
The army said on Friday that a fifth Turkish soldier was killed in northern Syria in clashes with Islamic State (IS) jihadists.
Seventeen Turkish soldiers have been killed since the military began an unprecedented operation in Syria on August 24 to back pro-Ankara rebels.
Turkish planes also carried out air strikes against seven IS targets in northern Syria, the army said in a statement on Friday carried by the state-run Anadolu news agency.
Turkey launched the operation in August -- dubbed "Euphrates Shield" -- in support of Syrian rebel fighters seeking to retake IS-held territory in northern Syria and also to halt the advance of Kurdish militia.
Since it began, the pro-Ankara rebels have captured the IS stronghold of Jarabulus, cleared IS from Al Rai and retaken the symbolically important town of Dabiq without much resistance.
They are now pressing to take Al Bab from the jihadists and will then move to Manbij to ensure there are no Kurdish militia members remaining, as agreed with Washington.
The battle to recapture Al Bab appears to be proving more difficult and violent as Dogan news agency reported on Friday evening that five more soldiers were injured after an IS attack.
They have been taken to the southeastern city of Kilis for medical treatment, Dogan said, adding that the total number of soldiers wounded in the day's action was seven.