The US says fighting between Turkey, pro-Turkish rebels and Kurdish-aligned forces in northern Syria is “unacceptable” and must stop.
Clashes in places where so-called Islamic State (IS) was not present were a “source of deep concern“, the US envoy to the anti-IS coalition tweeted.
Turkish forces have attacked what they say are Kurdish “terrorists” since crossing the border last week.
But the Kurdish YPG militia said Turkey just wants to occupy Syrian territory.
Ankara says it aims to push both IS and Kurdish fighters away from its border.
Turkish forces and allied factions of the rebel Free Syrian Army (FSA) forced IS out of the Syrian border city of Jarablus on Tuesday and have since pounded neighboring villages held by Kurdish-led, US-backed Syria Democratic Forces (SDF).
The Turkish military carried out 61 artillery strikes around Jarablus over the past 24 hours reports said.
Turkey has insisted Kurdish militia, which it regards as terrorists, retreat east across the Euphrates river.
The Kurdish Popular Protection Units (YPG), which dominates the SDF, says its forces have withdrawn, and that the Turkish action against the group was a “pretext” for occupying Syria.
The US Pentagon spokesman renewed Washington’s call for the YPG to pull back over the river, which he said had “largely occurred“.
He warned that uncoordinated operations “provide room for ISIL [IS] to find sanctuary and continue planning attacks against Turkey, the SDF, the United States, and our partners around the world“.
Turkish concern over Kurdish expansion increased after the SDF took control of the strategic Syrian city of Manbij from IS two weeks ago.