BEIRUT (AP) — France and the United States on Tuesday urged Turkey to exercise restraint in its offensive against a Kurdish-held enclave in northern Syria, where the U.N. says an estimated 5,000 people have been displaced by the fighting.

Turkish troops and allied Syrian fighters pressed ahead with their operations in Afrin for the fourth day, approaching from three sides and meeting stiff resistance from the U.S.-allied Kurdish militia that controls the enclave.

The U.N. said most of the displaced are still inside Afrin because Kurdish forces are preventing civilians from leaving and Syrian g...