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.