Some 100,000 people have fled their homes in north Syria, as Turkey presses on with its cross-border offensive on Kurdish-held areas.
The UN says, many people are sheltering in schools and other buildings, in the Hassakeh city and the town of Tal Tamer.
At least 11 civilians have died.
Turkey took action on Wednesday, after US President Donald Trump pulled American troops out of the area.
Much of the region has been outside the control of the Syrian government, as a consequence of the civil war which began in 2011.
The region has been controlled by the Kurdish-led Syrian Democratic Forces, since 2015.
The Syrian Democratic Forces have been key allies of the US, in the battle against the Islamic State, but Turkey regards the Kurdish militias of the Syrian Democratic Forces as “terrorists”, who support an anti-Turkish insurgency.