Thousands of civilians have fled an offensive by the Daesh terrorist group against the U.S.-backed moderate opposition in northern Syria, a monitor said on Sunday.

The offensive against the towns of Marea and Azaz threatens to overrun the last swathe of territory in the east of Aleppo province held by the opposition and bring Daesh to the doorstep of the Kurdish enclave of Afrin.

Daesh terrorists managed to cut the key supply line in a surprise assault early on Friday.

At least 61 rebel fighters have been killed in the fighting, as well as 47 terrorists, nine of them suicide bombers, the Observatory said.

Northwest of Azaz, a senior nurse said late Saturday that a hospital supported by Doctors Without Borders (MSF) was closed except for emergencies.

MSF said on Friday that it was evacuating patients and staff from the hospital in Salamah town as it was just three kilometers (two miles) from the front line.

The United Nations has expressed concern for some 165,000 civilians who have been trapped by the fighting between Azaz and the closed Turkish border.

The UN refugee agency said fleeing civilians were being caught in crossfire and were facing "challenges to access medical services, food, water and safety".

The supply lines to Turkey have made Aleppo province one of the most contested battlegrounds of Syria's five-year-old civil war.

Parts are held by the Assad regime, parts by moderate opposition, parts by the YPG and parts by Daesh or its rival Al-Qaeda.

At least 29 civilians have been killed since Daesh launched the assault early on Friday, the Syrian Observatory for Human Rights said.

It came as the terrorists were under attack by the YPG-led alliance in Raqqa province further east and by the army and allied militia around Fallujah in neighboring Iraq.

"More than 6,000 civilians, most of them women and children, were able to flee areas in the countryside of Aleppo province... especially from Marea town and Sheikh Issa village" to its west, the Britain-based monitoring group said.

An anesthetist who fled Marea with his family after five relatives were killed in shelling said late Saturday that just four medical staff remained in the town's only hospital.

He said Daesh surrounded the hospital for 10 hours on Friday, injuring two members of staff and forcing doctors to operate on one of them without electricity after Daesh cut off the hospital's generator.

Washington's support for the PKK-affiliated YPG has severely strained relations with NATO ally Ankara which regards it as a terror group. The PKK is recognized as a terrorist organization by the U.S. and the EU.

AFP pictures of US commandos wearing the YPG insignia drew condemnation on Saturday from President Recep Tayyip Erdoğan.