Kurdish militia has been a key US ally in the fight against Islamic State jihadist group in Syria.

(AFP) - Syria s Kurds vowed to fight to retake the Kurdish enclave of Afrin after Turkey-led fighters on Sunday seized control of its main city two months into a offensive.

"Resistance... will continue until every inch of Afrin is liberated and the people of Afrin return to their villages and homes," authorities in the semi-autonomous canton of Afrin said in a statement.

Turkish forces and alllied Syrian rebels on January 20 launched an operation against the Kurdish People s Protection Units (YPG) militia in the enclave.

As of Sunday afternoon, the whole of the Afrin enclave was in the hands of Turkey-led forces, said the Syrian Observatory for Human Rights, a Britain-based war monitor that relies on sources on the ground for its information.

"In all of Afrin s sectors, our forces will become a permanent nightmare" for pro-Ankara forces, the statement said.

"Our war against the Turkish occupation... has entered a new phase: a switch from direct confrontation to hit-and-run attacks," it said.

Turkey considers the YPG to be "terrorists", but the Kurdish militia has also been a key US ally in the fight against the Islamic State jihadist group in Syria.