In letters of complaint to the UN, Syria had earlier accused Turkey of allowing about 100 "Turkish soldiers or mercenaries" - to cross into Syria.
It urged the UN to take action against Turkish shelling in northern Syria, calling it a violation of sovereignty.
Turkey had shelled Kurdish forces over the weekend as they advanced in northern Aleppo province.
The Kurds have been capturing areas from Syrian rebel forces who are also fighting President Bashar al-Assad.
Ankara views the Kurdish militia in Syria as allied to the outlawed PKK, which has carried out a decades-long campaign for autonomy in Turkey.
Separately, the Turkish armed forces said one of its soldier was killed on Sunday evening in a border clash with a group seeking to enter Turkey illegally, Reuters reported.
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