The troops in Syria have been supporting the Kurdish-led Syrian Democratic Forces fight ISIS, but with the militant group all but defeated, the U.S. president made the surprise announcement of a total USA withdrawal on December 19.
President Recep Tayyip Erdoğan has called Bolton's remarks unacceptable, saying Turkey could not accept the U.S.' condition of protecting YPG terrorists, the Syrian affiliate of the PKK.
In a separate tweet, Trump also warned the Kurds against provoking Turkey.
After media reports suggesting the departure of United States forces had begun, the Pentagon later said no troops had yet withdrawn and stressed that the battle against ISIS was continuing as US-backed forces try to capture the group's last remaining pockets of territory in Syria.
USA national security adviser John Bolton suggested on Tuesday that protecting Washington's Kurdish allies would be a precondition of the U.S. withdrawal.
Speaking in Abu Dhabi later in the day, Pompeo said there were still many details to be worked out with Turkey but he was optimistic that a "good outcome" can be achieved that protects Turkey from legitimate terror threats, after speaking to the Turkish foreign minister.
"Russia, Iran and Syria have been the biggest beneficiaries of the long-term U.S. policy of destroying ISIS in Syria - natural enemies". "We also benefit but it is now time to bring our troops back home".
He said the US envoy for Syria, Jim Jeffrey, had traveled to northeast Syria this week and would soon go to Ankara for talks, including on moving forward a UN-led political process to end the eight-year long conflict in Syria. "Stop the ENDLESS WARS!" he continued.
Mr Trump's comments on Sunday followed further criticism of his abrupt decision to withdraw USA forces from Syria.
"It is a fatal mistake to equate Syrian Kurds with the PKK, which is on the United States terrorists list, and its Syria branch PYD/YPG", Ibrahim Kalin, Turkish presidential spokesperson said on Twitter in response to Trump's threat.
Observatory head Rami Abdel Rahman said that several dozen Islamist fighters were among those evacuated to areas held by the Kurdish-Arab alliance.
On Saturday, more than 600 people were evacuated from the remaining IS holdout in eastern Syria, a monitor said, as US-backed fighters prepared for a final assault on the area.
The US-led coalition on Saturday fired more than 20 missiles against jihadist positions, the observatory said.
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