Esper said President Donald Trump ordered U.S. forces to move south of the Turkish operation area, but not leave Syria.
"In the last 24 hours, we learned that [the Turks] likely intend to extend their attack further south than originally planned, and to the west," Esper said in a pre-taped interview with "Face the Nation" on CBS.
"We also have learned in the last 24 hours that the ... (Syrian Democratic Forces) SDF are looking to cut a deal, if you will, with the Syrians and the Russians to counterattack against the Turks in the north."
Esper said he spoke with Trump Saturday night, and that the president directed the U.S. military to "begin a deliberate withdrawal of forces from northern Syria."
Meanwhile, a small number of U.S. troops have left an outpost in the town of Ayn Issa in northern Syria because of concerns about a Turkish operation that is pushing into Syria, two U.S. defense official told Reuters on Sunday.
The officials, speaking on condition of anonymity, said the troops had moved because of concerns they could be caught in the middle of the Turkish operation.
The U.S. observation point south of Ayn al-Arab in northern Syria was evacuated on Sunday by 3 p.m., security sources said Sunday night.
Turkey launched Operation Peace Spring, the third in a series of cross-border anti-terror operations in northern Syria targeting terrorists affiliated with Daesh and the PKK's Syrian offshoot the People's Protection Units (YPG), on Oct. 9 at 4 p.m.
The operation, conducted in line with the country's right to self-defense borne out of international law and U.N. Security Council resolutions, aims to establish a terror-free safe zone for Syrians return in the area east of the Euphrates River controlled by the U.S.-backed Syrian Democratic Forces (SDF), which is dominated by YPG terrorists.
The PKK — listed as a terrorist organization by Turkey, the U.S. and the European Union — has waged a terror campaign against Turkey for more than 30 years, resulting in the deaths of nearly 40,000 people, including women, children and infants.
Turkey has long decried the threat from terrorists east of the Euphrates in northern Syria, pledging military action to prevent the formation of a "terrorist corridor" there.
Since 2016, Turkey's Euphrates Shield and Olive Branch operations in northwestern Syria have liberated the region from YPG/PKK and Daesh terrorists, making it possible for nearly 400,000 Syrians who fled the violence to return home.