The plane had been seeking to hit targets of Islamic State (IS) jihadists but by accident killed three soldiers
The plane had been seeking to hit targets of Islamic State (IS) jihadists but "by accident three of our heroic soldiers were martyred when a building was bombed where our units were," it said.
Russian President Vladimir Putin had already reached out to Turkish counterpart Recep Tayyip Erdogan to express his "sadness and condolences."
"Russian officials have said that the incident was an accident and have passed on their sadness and condolences," the army said, adding an investigation is being carried out by both sides.
It said that of the 11 injured, one was badly wounded.
In Moscow, the Kremlin said Putin had offered Erdogan his condolences and that the leaders had "agreed to enhance military coordination" going forward in the fight against IS in Syria.
Turkey on August 24 began an unprecedented campaign inside Syria against IS and Kurdish militia which initially made rapid progress but has become mired in a deadly fight for the IS held town of Al-Bab since December.
While Turkey gave no details over the location of the deadly incident, Moscow said that it took place around Al-Bab where Russian forces have also been conducting air strikes.
Before Thursday's casualties were reported, the Dogan news agency said 66 Turkish soldiers have now been killed in the Syria operation since it began in August, mostly in attacks by IS.
Turkey and Russia have been on sharply opposing sides in the Syria conflict, with Moscow supporting the regime of President Bashar al-Assad but Ankara pushing for his ouster as the key to peace.
Relations reached a dangerous low in November 2015 when Turkish warplanes shot down a Russian fighter jet over the Syrian border.
But a normalisation deal was reached over the summer and the two sides have been working ever more closely over the Syrian conflict.
They secured a deal to evacuate Syrians from Aleppo after the city was retaken by Assad backed by his Russian allies.
The two sides have since backed a process in the Kazakh capital Astana to search for peace to end the almost six-year civil war in Syria.
Meanwhile, separate operations by Turkey and Assad's forces, backed by Moscow, were trapping the jihadists inside Al-Bab.
Al-Bab has been besieged since Monday, when Assad's forces advancing from the south cut off a road leading into the town.