ANKARA, Turkey — Turkey sent more tanks into northern Syria on Thursday and gave Syrian Kurdish forces a week to scale back their presence near the Turkish border, a day after it launched a U.S.-backed cross-border incursion to establish a frontier zone free of the Islamic State and Kurdish rebels.

Skirmishes broke out between Turkish-backed Syrian rebels and the U.S.-backed Kurdish fighters, raising the potential for an all-out confrontation between the two American allies that would also jeopardize the fight against the Islamic State in the volatile area.

Turkey’s incursion Wednesday to capture the town of Jarablus was a dramatic escalation of Turkey’s role in Syria’s war and adds yet another powerhouse force on the ground in an already complicated conflict.

But Ankara’s objective went beyond fighting extremists. Turkey is also aiming to contain the expansion by Syria’s Kurds, who have used the fight against the Islamic State and the chaos of Syria’s civil war to seize nearly the entire stretch of territory along Syria’s northern border with Turkey.

Above all, Ankara seeks to avoid Kurdish forces linking up their strongholds along the border. The U.S. has backed its NATO ally, sending a stern warning to the Syrian Kurds with whom it has partnered in the fight against the Islamic State to stay east of the Euphrates River. The river crosses from Turkey into Syria at Jarablus.

“The U.S. is interested in stopping this from becoming a confrontation between the YPG and Turkey. That would be a huge detriment to the anti-IS campaign,” said Chris Kozak, a Syria researcher at the Washington-based Institute of the Study of War, referring to the main U.S.-backed Kurdish faction fighting the Islamic State. Turkey accuses the group of links to Kurdish groups waging an insurgency in southeastern Turkey.