Russian President Vladimir Putin has expressed his condolences in a telephone conversation with Turkish leader Tayyip Recip Erdogan.
A Russian warplane on Thursday accidentally hit a building in northern Syria with Turkish soldiers inside, killing at least three troops and wounding 11, Turkey's military said.
"Unfortunately, our military, while carrying out strikes on terrorists, was guided by coordinates given to them by our Turkish partners, and Turkish servicemen should not have been present on those coordinates", Mr Peskov said in a conference call with reporters.
Kremlin spokesman Dmitry Peskov said the air strikes had been launched based on coordinates provided to Russian Federation by the Turkish military.
They secured a deal to evacuate Syrians from Aleppo after Russia-backed regime forces retook the city, and have joined forces against the Islamic State group around Al-Bab.
The deaths from Thursday's airstrike raise the number of Turkish troops killed in Turkey's operation in Syria to 64.
The Turkish military said it regularly shared information with Russian counterparts on Syria operations as part of an agreement reached by the two countries on January 12 to "prevent units from harming each other".
Russian Federation is a major ally of Syrian regime leader Bashar al-Assad, while Turkey supports the rebels who oppose him. A second rebel official, a commander in the Al Bab area, added: "They opened fire".
Syrian government troops and allied militias, as well Turkish troops, the U.S-led worldwide coalition and Russian Federation have been going after IS in different parts of the country.
The clash has raised concerns that parallel offensives to take the city could ignite a new wave of fighting between government forces and Syrian rebels.
There was no immediate comment from Damascus on the reported clashes.