"We don't know what is going to happen", the UN's humanitarian coordinator for Syria, Panos Moumtzis, said in Geneva, stressing there were "a lot of unanswered questions" about the consequences of the operation.
The SDF says it has been "stabbed in the back" by the United States and will defend north-eastern Syria "at all costs".
The Syrian Democratic Forces (SDF), the Kurdish-led militia that controls much of northeastern Syria, said early Monday in a statement that "US forces withdrew from the border areas with Turkey".
The SDF accused Washington of betraying its ally.
But senior Republicans criticised the decision, with even staunch ally Mitch McConnell, the Senate Majority leader, saying: "A precipitous withdrawal of United States forces from Syria would only benefit Russia, Iran, and the Assad regime".
"Sometimes people that don't have the need to know or that aren't part of the decision chain may be a little disappointed that they weren't part of it and may call their friends in the press and tell them that they're blindsided", the official said.
The White House statement Sunday said Turkey will take custody of foreign fighters captured in the US-led campaign against the Islamic State group who have been held by the Kurdish forces supported by the US.
"We will fight where it is to our benefit, and only fight to win", he emphasized.
It has repeatedly warned of launching an offensive on its own into northeast Syria, where U.S. forces are stationed alongside the SDF. Turkey has previously said it wants to settle up to two million Syrian refugees in the zone.
Turkey has two main goals in northeast Syria: to drive the Kurdish YPG militia which it deems a security threat away from its border, and to create a space inside Syria where two million Syria refugees now hosted in Turkey can be settled. Turkey has demanded USA -allied Syrian Kurds leave the area.
Turkish state media also reported on military reinforcements sent to the border with Syria after Erdogan's comments.