The decision brought condemnation from Democrats and Republicans.
Trump says U.S. troops completed their mission in Syria of fighting the Islamic State movement.
Graham later stated, "Well, it's a lie that the - that ISIS has been defeated".
Turkey says it wants to set up a 480km (300 mile) long and 30km deep "safe zone" along its border with Syria, to resettle up to two million of the more than 3.6 million Syrian refugees now living in Turkey.
French President Emmanuel Macron met on Tuesday with Jihane Ahmed, the spokeswoman for the Kurdish-led Syrian Democratic Forces (SDF), according to the president's office. The move by Trump on Sunday has been interpreted as clearing the way for Turkey to attack those forces.
But others - among them some of the most faithful advocates for Mr. Trump's foreign policy - warn that the Syria decision will weaken the US image as a reliable ally and only buoy its adversaries in the region - from Iran to the remnants of ISIS that remain in the region and which have recently shown renewed signs of life.
Iran, another Assad ally, voiced opposition to any Turkish military operation in Syria.
Two mortar shells were fired from YPG/PKK-occupied Rasulayn in Syria to Ceylanpinar district in Turkey's border province of Sanliurfa.
Who are the Kurdish forces?
Ankara regards the YPG as a terrorist group affiliated with the Kurdistan Workers' Party (PKK), which has fought the Turkish state for more than three decades.
"I urge President Trump to change course while there is still time by going back to the safe zone concept that was working", said Graham, who also took his message to "Fox and Friends", a favorite show of the television-loving U.S. leader.
Turkey designates Kurdish groups in southern Turkey and northern Syria and Iraq as terrorist organizations.
On Monday, Erdogan said US troops started to pull back after a call he had with Trump, adding talks between Turkish and USA officials on the matter would go on. "We are helping the Kurds financially/weapons!" But the U.S. backs the YPG and credits the Kurds for helping defeat ISIS in Syria.
Turkey had been poised to advance into north-east Syria since US troops began vacating the area in an abrupt policy shift by US President Donald Trump, widely criticised in Washington as a betrayal of America's Kurdish militia allies. The comments were made by a senior administration official during a call to reporters on Monday.
Since then, the United States has continued to provide support to the mainly-Kurdish SDF, as they engage in additional clearing operations against IS remnants and sleeper cells across northeastern Syria.
Trump has pointed to the defeat of ISIS as a reason to withdraw, but for months ISIS has been regrouping and gathering more steam, according to reports.
"The Turkish military is shelling one of our points on #SereKaniye Border with Turkey", the SDF said in a tweet late Tuesday, referencing Ras al-Ain.
On Tuesday, a U.S. official said U.S. Defense Secretary Mark Esper and Chairman of the Joint Chiefs of Staff General Mark Milley took part in the phone call, but the official did not provide further details.
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.
One of the big question marks surrounding Turkey's plans is whether fighting the Syrian Kurdish forces would allow IS to make a comeback. That would actually be a sign of real leadership.
While Iraqi forces are "focused on containing the protest movement in the cities", Wahab said, "Kurdish and Iraqi forces are yet to reach the kind of security deal that would deny ISIS a safe haven for a resurgence". This poses serious threats to our security.
The U.S. move will leave Kurdish-led forces long allied to Washington vulnerable to attack by the Turkish Armed Forces (TSK).