The rebels advanced east from the town of Al-Bab, which they captured last week from the Islamic State (IS) jihadist group, into territory controlled by the Syrian Democratic Forces.
The SDF is dominated by the Kurdish People's Protection Units (YPG), which Ankara considers a "terrorist" organisation.
Syrian rebels "captured the villages of Tal Turin and Qara east of Al-Bab after violent clashes with the separatist YPG militia", according to a statement today by Hiwar Kallis, a rebel faction.
Control of Aleppo province is divided between a myriad of armed groups -- rebels, jihadists, Kurdish militia and Syrian government forces.
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After capturing Al-Bab last Thursday, the rebels' only front lines were with the SDF and Syrian government forces.
Turkish President Recep Tayyip Erdogan said Monday that the next target after Al-Bab would be Manbij -- a former bastion of IS that is now under the control of the US-backed SDF.
"Euphrates Shield attacked our forces today, and the clashes are ongoing," said Sherfan Darwish, spokesman for the Manbij Military Council which is part of the SDF.
"These battles mark the beginning of Euphrates Shield's operations to take Manbij," said the monitoring group's head Rami Abdel Rahman.
Turkey has also set it sights on Raqa, the de facto Syrian capital of IS's so-called "caliphate".
Turkish Defence Minister Fikri Isik said Ankara is prepared to join an international coalition to take the IS fiefdom but only if the YPG are not involved.