"Our military while launching strikes on terrorists followed coordinates that were given to us by our Turkish partners", Kremlin spokesman Dmitry Peskov told journalists.
He said there had been a communications failure, adding: "There should not have been Turkish soldiers within the limits of these coordinates".
Russia immediately apologized for the bombing near the Islamic State-held town of al-Bab, which came amid warming ties between Turkey and Russia after they were strained by Turkey's downing of a Russian jet near the border with Syria two years ago.
The "friendly fire" incident occurred during an operation against Daesh near the northern Syrian city of al-Bab on Thursday, highlighting the risk of unintended clashes between the numerous outside powers in a complex war.
"Our units hit by the (Russian) plane on February 9 have been located on the same spot for approximately 10 days", the military said. One of them said government forces had moved towards their positions in tanks.
It was not immediately clear whether the confrontation described by the sources had taken place in the same area as the air strike that killed the Turkish soldiers.
The Britain-based Syrian Observatory for Human Rights said the clashes were fierce in the area, where government troops made a significant advance Thursday.
Russian Federation is a key ally of Syrian President Bashar Assad, while Turkey supports the rebels who oppose him. There was no immediate comment from Russian Federation.
Turkish Prime Minister Binali Yildirim said earlier this week that clashes with Syrian forces had been avoided thanks to global coordination, including that between Turkey and Russian Federation.
Syrian government troops and allied militias, as well Turkish troops, the U.S-led global coalition and Russian Federation have been going after IS in different parts of the country.