Al-Bab is 40 kilometers (25 miles) south of the Turkish border. The Kremlin spokesman said that Putin told Erdogan that Turkish soldiers had died as a result of lack of coordination regarding coordinates during Russian military jets' strikes in Syria.
Turkey's military forcers and allied rebels in Syria continued their offensive against the town of Tel Rifaat in northern Aleppo, targeting positions of the Kurdish-led Syrian Democratic Forces (SDF), local sources reported on Wednesday.
The statement came as Turkey's Hurriyet newspaper reported that rebel forces and those of Syrian President Bashar al-Assad have created a security corridor to avoid clashes around al-Bab.
The YPG said they fired warning shots at Turkish forces who attempted to cross the border into Rojava, northern Syria near Elok village.
"Daesh forces have begun leaving al-Bab completely", he said, using an Arabic acronym for the Islamic State (IS) group. "The chiefs of the [Russian and Turkish] general staffs agreed to closer coordinate joint actions and exchange information about the situation on the ground".
The report noted that the General Staff has cleared large part of Al-Bab from terrorists and continue the operation.
Militants of the YPG, the armed branch of the PYD, said clashes have flared up frequently in recent days due to attempts at trespassing by Turkish army forces and pro-Turkish Syrian militants.
FSA forces, which are being backed by Turkish artillery and air strikes, have been trying to capture al-Bab from ISIL since December previous year.
The news comes as the Turkish military operation in Syria's al-Bab has entered the final stage. Al-Bab is one of Daeshs last remaining strongholds near the Turkish border.