The statement added the leaders agreed to step up military coordination during operations in Syria against Daesh and other extremist groups.
President Vladimir Putin promptly called his Turkish counterpart, Recep Tayyip Erdogan, to express regrets over the friendly fire incident.
As for the Turkish forces, the troops are aiming to divert the attention of the IS militants inside the city, by heavily shelling al-Bab by airstrikes and artillery shelling.
Turkey and Russian Federation back opposing sides in the war, but have joined forces in recent months to try to end the conflict.
The Turkish military said on Thursday it had killed 44 militants in aerial and artillery strikes and clashes in northern Syria. Three of the soldiers were killed and 11 others were wounded.
Turkish-backed Syrian rebels have pushed into the ISIS-held city of al-Bab in northern Syria, BBC News reported.
A Syrian rebel official and a monitoring organization said the advancing rebel and Turkish forces had captured the western outskirts of al-Bab, some 30 km (20 miles) south of the Turkish border.
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Turkey had 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.
Russia and Turkey only recently repaired ties after Turkey shot down a Russian jet near the border with Syria two years ago.
Turkey and Russian Federation have clashed over other deadly incidents involving the military.
A Syrian rebel fighter reached by Reuters said he was speaking from inside al-Bab where ISIL lines were "collapsing".
Syrian government forces have also advanced on it from the south, bringing them close to their Turkish and rebel enemies.
The Syrian army and allied fighters have become less than three kilometers from al-Bab, said the report.
Russian Federation began its military intervention in the Syrian civil war in September 2015.