"Pro-Turkish militants attacked the villages of Ain Daqna and Belule where YPG and YPJ [female division] were lying in wait. Eighty-three militants were killed in a fierce fight that followed," the command said.
The Kurdish forces have published videos that allegedly showed the bodies of killed Syrian militants. The militia did not disclose their casualties.
The Turkish and allied rebels from the Free Syrian Army launched an operation last Saturday, called Olive Branch, to crush YPG forces which Ankara accuses of ties to the banned Kurdistan Workers Party (PKK), a pro-independence group in Turkey.
Since the beginning of the military operation, the Turkish military and Kurdish representatives have been sharing conflicting reports concerning the situation in the region.
YPG said earlier that no more than 15-20 Kurdish militiamen had been killed, while the Turkish military reported that hundreds of militants had been killed in the campaign.