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 says 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 neighbouring villages held by Kurdish-led, US-backed Syria Democratic Forces (SDF).
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The Kurdish Popular Protection Units (YPG), which dominates the SDF, says its forces have withdrawn, and that the Turkish action against the group was a "pretext" for occupying Syria.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 unco-ordinated 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 two weeks ago.
Turkey has been fighting a Kurdish insurgency in its south-east for decades and fears Kurdish gains in northern Syria will fuel Kurdish separatism at home.
On Sunday, tens of people were killed in Turkish air strikes on Kurdish-held areas near Jarablus.
A monitoring group said at least 35 civilians and four militants had been killed, while the Turkish military said 25 people, all Kurdish militants, died.
Analysis: Guney Yildiz, BBC News
Turkey's coming into conflict with the Kurdish People's Protection Units (YPG) or their Arab allies complicates its military campaign.
Ankara wants to force the Kurds to withdraw to the east of the Euphrates River, stopping short of establishing a corridor to link two Kurdish-led areas in north-western Syria.
Turkey enjoys tacit support from Russia, the Assad government and Iran in acting to prevent further territorial gains by the Kurds and their allies. The US, on the other side, has said it will try to prevent Turkey coming into conflict with its allies in the region.
A possible Turkish campaign against the Kurds in Syria could also risk igniting further clashes with the Kurdistan Worker's Party (PKK) militants inside Turkey. The PKK recently upped its attacks significantly in correlation with the Turkish operation inside Syria.
US anti-IS coalition envoy Brett McGurk tweeted from a Defense Department briefing, saying the US "was not involved in these activities, they were not coordinated with US forces and we do not support them.
"Accordingly, we call on all armed actors to stand down and take appropriate measures to deconflict and open channels of communication."
Turkey is a US Nato ally and member of the anti-IS coalition, but the US support for the YPG has put it at odds with Washington.