Syria war: US warns over Turkish-Kurdish violence
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.
US President Barack Obama will meet his Turkish counterpart Recep Tayyip Erdogan in China on Sunday, ahead of the G20 summit there, and will discuss Syria, the White House said.
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 Wednesday and have since pounded neighbouring villages held by Kurdish-led, US-backed Syria Democratic Forces (SDF).
The Turkish military had carried out 61 artillery strikes on 20 targets around Jarablus in 24 hours, Turkey's state news agency Anadolu reported on Monday.
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The Kurdish Popular Protection Units (YPG), which dominates the SDF, says its forces have withdrawn, and that the Turkish action against the group was a "pretext" for occupying Syria.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 Defence Secretary Ash Carter said the YPG "will and is withdrawing" east of the Euphrates.
He called on Turkey to stay focused on the fight against IS and not to engage the SDF.
He said the US was "very supportive" of Turkey's general counter-IS activities and its efforts to secure the border - but not the area south of Jarablus.
Turkish concern over Kurdish expansion increased after the SDF took control of the strategic Syrian city of Manbij from IS two weeks ago.
Analysis: Gary O'Donoghue, BBC News, Washington
The liberation of Jarablus - the last remaining IS stronghold on the Turkish border - should have been cause for celebration for the US, Turkey and the groups fighting jihadist militants in northern Syria. Instead it's opened up a whole new set of potential conflicts between Turkey and the Kurdish militias, with the US stuck in the middle.
Washington has long seen the Syrian Kurdish YPG forces as among the most capable in the fight against IS and has supplied training and weaponry to them. But its Nato ally, Turkey, has taken a dim view of that backing.
Add to all that the recent coup attempt in Turkey - which Ankara believes the US was far too slow to condemn - and there's a significant risk of increased instability in a region already torn apart by five years of civil war.
The US always knew the coalitions it was putting together in this part of the world would be fragile - it will now have to use all its diplomatic might to hold things together.
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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.
Turkish-backed forces moved towards Manbij, 20 miles (30 km) south of Turkey's border, on Monday, Reuters reported.
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.
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."