Rebels backed by Turkey have driven US-allied Kurdish forces from a number of towns and villages in northern Syria with Ankara looking to push the militants east of the Euphrates River in an operation which has so far claimed at least 35 civilian lives.
The Kurdish Democratic Union Party has condemned what it said was international silence regarding "Turkish occupation" of Syria, the Daily Mail reported.
Turkey's involvement in the Syrian civil war last week was aimed at helping the Syrian rebels drive the IS out of the border town of Jarablus.
On Tuesday, the US Pentagon described clashes between Turkish and Kurdish forces in Syria as "unacceptable" and called on all sides to "stand down".
"We are closely monitoring reports of clashes south of Jarabulus -- where IS is no longer located -- between the Turkish armed forces, some opposition groups, and units that are affiliated with the SDF (Kurdish-led Syrian Democratic Forces)," he said.
"We want to make clear that we find these clashes unacceptable and they are a source of deep concern."
Speaking at a rally in the border town of Gaziantep, Turkish President Recep Tayyip Erdogan said his military is committed to fighting terrorism in Syria and Iraq to "uproot" the Syrian Kurdish group, calling it a terrorist organisation.
Turkey is part of the US-led coalition fighting the IS, but the air strikes that began on Saturday marked the first time it has targeted Kurdish-led forces in Syria.
