More than 150,000 civilians have fled the city of Afrin in northern Syria since Wednesday evening to escape a Turkish-led military offensive against a Kurdish militia, a war monitor said.

"There was fierce fighting throughout the night on the northern outskirts of the city as the Turkish forces and their Syrian allies tried to break into the city," the Syrian Observatory for Human Rights said on Saturday.

Turkey and its Syrian Arab rebel allies have waged a nearly two-month offensive on the Afrin enclave, which is held by the Kurdish People's Protection Units (YPG).

Earlier this week, they largely surrounded the enclave's sole city, which was home to some 350,000 people, including people displaced from other parts of the enclave already overrun.

A single escape route remains open to the south to territory still held by the YPG or controlled by the Damascus government.

"Civilians are fleeing through the southern corridor," Observatory director Rami Abdel Rahman told AFP.

Afrin has come under heavy air and artillery bombardment by the Turkish army.

On Friday evening, a Turkish bombing raid struck the city's main hospital, killing 16 civilians, a monitor said.

Turkey's military denied hitting the hospital, saying that its operation in Afrin "is carried out in such a way as to not cause any harm to civilians."