Three Turkish soldiers were mistakenly killed and 11 were injured in a Russian airstrike near the Syrian city of al-Bab, the Turkish armed forces said Thursday. One of them said the government forces had moved towards their positions in tanks.
Putin contacted Erdogan to express his "sadness and condolences", it added.
Both countries are conducting a joint investigation, Turkey's military said.
The two countries have since repaired relations, and the Kremlin statement on Thursday said the two leaders had agreed to step up military coordination against Daesh terrorist group.
Dmitry Peskov, the Kremlin spokesman, said on Friday that "there should not have been Turkish soldiers within the limits of these coordinates".
Tensions were further strained in December when the Russian ambassador to Turkey was assassinated at an art gallery in Ankara.
Russia's Defense Ministry said Chief of the General Staff Valery Gerasimov also called his Turkish counterpart to offer condolences over the accidental strike.
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The White House - which had declared the raid "a successful operation by all standards" - had no comment Monday on his escape from death.
Turkey and its FSA rebel allies have carved out a de facto buffer zone in northern Syria in territory captured from Islamic State since August in their "Euphrates Shield" operation.
"According to initial information we received, it is a total accident but how it happened and how the coordination was miscalculated will be clarified".
The Syrian ceasefire excluded areas where militant factions, IS and Syria's al-Qaida affiliate, operate or hold ground.
Moscow has been flying a bombing campaign in Syria in support of the forces of Syrian President Bashar al-Assad since 2015.
Turkish Prime Minister Binali Yildirim said earlier this week that clashes with the Syrian forces had been avoided thanks to global coordination, including between Turkey and Russian Federation.
But a normalization deal was reached over the summer and the two sides have been working ever more closely over the Syrian conflict.
The two sides have since backed a process in the Kazakh capital Astana to search for peace to end the nearly six-year civil war in Syria.