ANKARA, Turkey — Syrian Kurdish forces have started withdrawing east of the Euphrates River, Turkish officials said Thursday, a move that could fulfill a major demand by Ankara and the United States a day after Turkey sent in tanks across the border to help Syrian rebels take a key Islamic State stronghold.

The Turkish officials were quoting U.S. Secretary of State John Kerry, who relayed the news in a telephone conversation with his Turkish counterpart.

Turkey’s surprise incursion Wednesday to capture the town of Jarablus was a dramatic escalation of Turkey’s role in Syria’s war. But Ankara’s objective went beyond fighting extremists. Turkey is also aiming to contain the expansion by Syria’s Kurds, who are also backed by the United States and have used the fight against IS and the chaos of Syria’s civil war to seize nearly the entire stretch of the border with Turkey in northern Syria.

U.S. Vice President Joe Biden flew into Ankara hours after the offensive was launched, and he backed Turkey with a stern warning to the Kurds to stay east of the Euphrates, which crosses from Turkey into Syria at Jarablus.