The withdrawal from key positions along Syria's northern border came after the White House said it would step aside to allow for a Turkish operation President Recep Tayyip Erdogan has warned could come at any moment. For years, the Kurds have been close allies to the United States in the fight against ISIS.
Turkey hosts more than 3.6 million Syrians who fled the civil war that has raged in their country since 2011.
While a Kurdish-led operation earlier this year saw the death of IS's territorial caliphate, the organisation isn't dead and sleeper cells have been active in several parts of Syria and Iraq.
Syria's Kurds warned on Monday a Turkish military invasion would spark a major ISIL resurgence and vowed to battle Turkey's military.
"We will not abandon our land and we will stay here - but we do not want war", said Ahmed Mohamed Salem, a 52-year-old protester. "We will contribute to peace, peace and stability in Syria".
Erdoğan and Trump on October 6 exchanged views on bilateral issues as well as the planned safe zone east of the Euphrates River in northern Syria in a phone call, according to a statement from Turkey's Directorate of Communications.
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Much of the fighting with ISIS was carried out by the largely Kurdish Syrian Democratic Forces, who have expressed alarm at a US withdrawal from northern Syria, as it leaves them open to attack from Turkey.
Turkey wants to act before winter conditions make it hard for tanks to operate in muddy terrain, leaving little room for a last-minute agreement with the U.S.
"Security (in Turkey) can not be created through (military) action against Syria's territorial integrity and sovereignty", the Iranian top diplomat went on to say.
"They must, with Europe and others, watch over the captured ISIS fighters and families", he said after the White House announced that Turkish forces will soon be launching military operations in Northern Syria and American troops would withdraw from the region.
As US President Donald Trump sought to assuage concerns about the fate of the Kurds following impending US withdrawal from eastern Syria, he boasted of his "great and unmatched wisdom" in making the decision.
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Turkey's Foreign Minister Mevlut Cavusoglu said Turkey has supported Syria's territorial integrity since the beginning of the country's conflict, "and will continue to do so".
Mustafa Bali, the SDF spokesman, tweeted that his group is not expecting the U.S.to protect northeastern Syria.
"As the Syrian Democratic Forces, we are determined to defend our land at all costs", it said in a statement posted on social media.
And Nato allies had tentatively agreed, in August, to create a safe zone for refugees near the Turkish border.
Turkey considers the YPG an extension of the banned Kurdistan Workers' Party (PKK) which has fought for Kurdish autonomy in Turkey for three decades.
The two countries are also at odds over how far the zone should extend into Syria and who should control it. Turkey says it should be 30 km (19 miles) deep.
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Trump's move to pull out U.S. troops from Syria's northern border has been slammed by even his traditional national security and foreign policy supporters like Indian-American Nikki Haley.