Islamic State fighters have been fleeing the Syrian city of Manbij with their families as U.S.-backed groups advance to within 4 miles in an attack that has killed more than 150 jihadists, a spokesman for the U.S.-backed forces said.

Sharfan Darwish, spokesman for the Manbij Military Council, told Reuters on Monday more than 50 of their bodies were in the possession of the U.S.-backed Syria Democratic Forces (SDF) that is leading the campaign that got under way last week.

He said there were a number of dead among the U.S.-backed forces and the number would be announced later.

"There are many, many homes in Manbij that Daesh (Islamic State) had seized and were living in that are now empty. They took everything they could and left the city," Darwish said, citing reports from the city.

Reuters could not independently confirm the account.

The SDF, including the powerful Kurdish YPG militia, launched the attack last week with the ultimate aim of denying Islamic State its last foothold at the Syrian-Turkish frontier.

Darwish said the attack, supported by U.S. special forces, was proceeding according to plan.

"To be frank, if we had wanted to reach (Manbij) before this time, or if we wanted to arrive directly, we could have, but as you know the area is vast and there are a large number of civilians," he said.

"The progress is as it should be according to the plan."

Darwish confirmed the death of the commander of one of the armed groups taking part in the offensive, Faysal Abu Layla of the Sun of the North Battalions. He had died of wounds inflicted by a mortar bomb, he said.