Turkey has warned predominantly Kurdish Syrian forces of more strikes by Turkish forces unless they withdraw east of the River Euphrates immediately.
Turkey's foreign minister Mevlut Cavusoglu spoke as Syrian opposition groups reported that Turkish-backed Syrian rebels have captured more towns and villages in northern Syria.
Turkish tanks rolled across the border last week to help Syrian rebels seize the town of Jarablus from the Islamic State group, a move that was also aimed at deterring further advances by Kurdish-led forces.
The fighting pits Turkey, a Nato ally, against a US-backed proxy that is the most effective ground force battling IS militants in Syria's five-year-old civil war.
It leaves Washington in the tough spot of having to choose between two allies, and is likely to divert resources from the fight against IS.
President Barack Obama will meet the president of Turkey next week when he travels to Asia for meetings with world leaders.
The White House said Mr Obama and Recep Tayyip Erdogan will meet on Sunday on the sidelines of a major economic summit. The two will discuss Turkey's recent assault against the Islamic State group in Syria and rising tensions with Kurds in the region.
Both Turkey and the United States have ordered the main Kurdish fighting force, the Kurdish People's Protection Units, or YPG, to withdraw to the east bank of the Euphrates.
"The YPG has to immediately cross east of the Euphrates River as they promised the United States and as they announced they would," said Mr Cavusoglu.
"If they don't, they will be a target."
The Kurdish-led force known as the Syrian Democratic Forces crossed the Euphrates earlier this month and drove IS militants out of Manbij, a key supply hub south of Jarablus, after a 10-week campaign.
Both Turkey and the United States have ordered the YPG militia to withdraw to the east bank of the river.
YPG leaders say they have, but their units advise the Syrian Democratic Forces, and it is not clear if any remain west of the Euphrates.
Syrian opposition activists have said that at least 35 civilians were killed in northern Syria in the Turkish-led operation so far.
Turkey denied any civilians had been hit.
A Turkish soldier was killed by a Kurdish rocket attack on Saturday, becoming the first such fatality in Turkey's ground offensive.
The Britain-based Syrian Observatory for Human Rights said the Turkey-backed rebels have captured 21 towns and villages near Jarablus from the Syria Democratic Forces.
The Observatory also reported clashes on Monday between the rebels and IS fighters on the western edge of Jarablus.
The Local Coordination Committees, an activist collective, said the rebels had captured seven more villages since late on Sunday.