The Kurdish-led Syrian Democratic Forces (SDF) said on Sunday they had withdrawn from the border town of Ras al-Ain under a U.S.-brokered ceasefire deal, but a spokesman for Turkish-backed Syrian rebels said the withdrawal was not yet complete.

Ras al-Ain is one of two towns on the Turkish-Syrian border that have been the main targets of Turkey's ongoing offensive to push back Kurdish fighters and create a "safe zone" more than 30-kilometer deep inside Syria.

Turkey paused the offensive on Thursday night for five days under a deal agreed between Turkish President Tayyip Erdogan and U.S. Vice President Mike Pence. Erdogan has warned that Turkey will resume the assault when the deadline expires on Tuesday if the SDF had not pulled back from the safe zone.

"We don't have any more fighters in the city," SDF spokesman Kino Gabriel said, referring to Ras al-Ain. His comments came after Ankara said dozens of vehicles had entered and left Ras al-Ain, which is largely surrounded by Turkish forces and their Syrian rebel allies, over the weekend.

Rebel spokesman Major Youssef Hamoud told Reuters that the SDF had "not yet completely" pulled out of Ras al-Ain.

Turkey launched its offensive after U.S. President Donald Trump announced he was withdrawing U.S. troops from northeastern Syria. His move was criticized in Washington and elsewhere as a betrayal of Kurdish allies who had fought for years alongside U.S. troops against ISIL.

Pentagon says up to 1,000 U.S. troops to withdraw from northern Syria

Ankara is seeking to set up the safe zone as a buffer, as it regards the YPG, the main component of the SDF, as a terrorist group because of its links to Kurdish insurgents in southeast Turkey. The YPG has been a close U.S. ally in the fight against ISIL.

U.S. Defense Secretary Mark Esper said roughly 1,000 U.S. troops withdrawing from the northeastern Syria will be repositioned into western Iraq, according to a transcript released by the Pentagon on Sunday.

"The U.S. withdrawal continues apace from northeast Syria. Again, we're talking weeks not days. We want to be very deliberate and very safe as we go about it," Esper told reporters on Saturday en route to Afghanistan. 

Based on the "current game plan," those troops will be repositioned into western Iraq to help defend the war-torn country and perform a counter-the ISIL mission, the Pentagon chief added.

Trump said last week that the U.S. troops leaving Syria will remain in the Middle East region to "monitor the situation," while a small number of U.S. forces will remain at At Tanf Garrison in southern Syria to counter the remnants of the ISIL.

(With input from agencies)