On Tuesday, Turkish officials told Reuters that the military had struck the Syrian-Iraqi border to prevent Kurdish forces using the route to reinforce the region, though details of the strikes were hazy.
Late Sunday, the White House abruptly announced it was pulling troops away from the border and that Turkey planned to launched an offensive - a major shift in USA policy that followed a phone call between President Trump and Erdogan.
Turkey fears that a pro-PKK entity on its southern border would inevitably become a launchpad for attacks on Turkey and, therefore, sees it as an existential threat.
In its call for mobilization, the local Kurdish authority known as the Autonomous Administration of North and East Syria also urged the global community to live up to its responsibilities as "a humanitarian catastrophe might befall our people" in the region.
The US announced on Monday it was withdrawing its troops from the region, effectively abandoning the Syrian Democratic Forces (SDF), its main ally in the battle against the Islamic State of Iraq and the Levant (ISIL, also known as ISIS).
President Donald Trump says he is unconcerned about ISIS fighters escaping Syrian prisons following the US pullout because "they will be escaping to Europe".
The abrupt move, announced in a Sunday night statement from the White House press secretary following a call between Trump and Erdogan, has prompted a rare show of bipartisan opposition to the Republican President. The group's leaders told the Times that there have been no discussions with us officials about turning over the camps to Turkey.
"We call upon our people, of all ethnic groups, to move toward areas close to the border with Turkey to carry out acts of resistance during this sensitive historical time, " it said, adding that the mobilization would last for three days.
Florida Rep. Donna Shalala called Trump's decision to withdraw troops from Syria "the worst kind of betrayal" of the Kurds, whom the US had vowed to protect. Turkey's announcement that an operation was underway followed Trump's announcement.
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The SDF, which has vowed to defend itself against any perceived Turkish incursion, called on the US-led coalition and the global community to implement a no-fly zone over northern Syria similar to the one implemented in Iraq.
In his statement, President Trump explained the rationale for the withdrawal, reiterating that the United States doesn't endorse Turkey's offensive in Syria.
Syria's Foreign Ministry condemned Turkey's plans for an invasion, calling it a "blatant violation" of global law and vowing to repel the incursion.
Kurdish leaders said they would hold their erstwhile U.S. ally and the whole global community responsible for any "humanitarian catastrophe".
Russian Foreign Minister Sergey Lavrov, meanwhile, accused the US of playing "very risky games" with the Syrian Kurds. Russian news said Moscow has communicated that position Washington.
Mr Graham predicted "a devastating ripple effect" from Turkish action in Syria, warning that Mr Trump's decision to withdraw the troops opened the way for a Turkish strike on Kurdish-led forces long allied with Washington.
President Tayyip Erdogan's communications director Fahrettin Altun said YPG fighters could either defect or Ankara would have to "stop them from disrupting" what he described as Turkey's struggle against Daesh militants.
Syrian Democratic Forces - a coalition formed with U.S. assistance in 2015 with Arab and Turkmen and other ethnic groups in northern Syria, the group has been a key fighter against the Islamic State (IS) group.
Isis has already claimed a twin suicide attack in the early hours of Wednesday in its former capital Raqqa which killed and injured 25 people. There were no immediate reports of casualties there. Military cargo planes also intermittently landed at the base.