Beirut: Islamic State appeared to have shunned an offer for its fighters to withdraw safely from the Syrian city of Manbij and clashes with U.S.-backed forces raged ahead of its expiry, a spokesman for Washington-backed forces said on Saturday.

The Syria Democratic Forces alliance, made up of Arab and Kurdish fighters and backed by the United States, made rapid advances against the jihadists last month after launching a campaign to flush them out of territory along the Turkish border, through which they had for years moved weapons and fighters.

The SDF quickly surrounded Manbij, but the fight to take the city has been tougher, with slow advances inside it in recent weeks.

On Thursday the SDF-allied Manbij Military Council said Islamic State militants would be allowed to leave the city with light weapons, without a fight, if their departure took place within 48 hours.

The offer had been initiated by local actors, the Council's spokesman Sharfan Darwish said, without elaborating.

"The deadline is approaching, time is almost up ... and the battles are continuing. As far as we're concerned, the situation has not changed," he said on Saturday, adding that there had been no apparent response from IS to the initiative.

"Our steps towards liberating Manbij are going ahead."

The British-based Syrian Observatory for Human Rights said clashes continues inside Manbij, and that the U.S.-led coalition fighting IS was bombing parts of the city and areas nearby.

Activists say dozens of civilians have been killed this week in air strikes in the city and to the north, and the opposition Syrian National Coalition called for a suspension of the air strikes while the incidents are investigated.