The SDF said it lost 11,000 of its forces over five years as it battled Islamic State.
"US forces on the ground showed us that this is not how they value friendship&alliance," SDF spokesman Mustafa Bali tweeted. "However, the decision by the @POTUS (Trump) is about to ruin the trust and cooperation between the SDF and US built during the fight against ISIS. Alliances are built on mutual trust."
The Syrian Observatory for Human Rights, a Britain-based war monitor, said US coalition forces withdrew at dawn from Ras al-Ain and the strategic Syrian town of Tal Abyad, located in northern al-Raqqa province near the Turkish border.
SDF's general command said any Turkish assault "will have a significant negative impact on our war against (Islamic State)."
This would be Turkey's third offensive in Syria, after Operation Euphrates Shield in 2016 and Operation Olive Branch in 2018.
Bali said Washington owes them an explanation about what happened to the buffer zone agreement. The SDF had agreed to dismantle its defensive positions in what would be the buffer zone in return for the US preventing a Turkish offensive.
In August, the US and Turkey agreed to set up a buffer zone in north-eastern Syria. Ankara was pushing to remove US-backed Syrian Kurdish forces there, which it claims are tied to the Kurdistan Workers' Party (PKK) waging an insurgency within Turkey, and resettle 1 million-2 million Syrian refugees.
Turkey repeatedly criticized the US of stalling on the zone, although both sides conducted joint aerial and ground patrols.
While the European Union warned Turkey against the offensive, the UN said it was concerned about the impact on the 1.7-million-strong civilian population in the area.
Turkey has not elaborated on the scope of its operation, but Erdogan reiterated on Monday: "We said we could enter anytime -- we are continuing our determination."