The United States has said that 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).
The Turkish military carried out 61 artillery strikes around Jarablus over the past 24 hours Reuters news agency 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The Kurdish Popular Protection Units (YPG), which dominates the SDF, says its forces have withdrawn, and that the Turkish action against the group was a “pretext” for occupying Syria.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 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 from IS 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.
Turkish-backed forces moved towards Manbij, 20 miles (30 kilometres) 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.