US-backed Syrian fighters have surrounded the Islamic State (IS) group-held city of Manbij from three sides as they press an offensive against the militants near the Turkish border, a spokesman for the fighters said on Monday.

The Syria Democratic Forces (SDF), including the powerful Kurdish YPG militia and Arab allies, launched the attack last week with the ultimate aim of dislodging Islamic State from its last foothold at the Syrian-Turkish frontier.

The Syrian Observatory for Human Rights, a Britain-based group that reports on the war, said the US-backed forces had cut the road north from Manbij to IS group-held Jarabulus at the Turkish border, which is also expected to be targeted.

Sharfan Darwish, spokesman for the Manbij Military Council, said the US-backed alliance had advanced to within 6 km (4 miles) of Manbij, and the attack backed by US special forces was going to plan. Over 150 militants had been killed, with 50 of the bodies in SDF hands, he said.

"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. "Our forces are surrounding Manbij from three directions."

He said there were dead among the SDF and the number would be announced later. They included the commander of one of the groups, Faysal Abu Layla of the Sun of the North Battalions. He had died of wounds caused by a mortar bomb.

The Syrian Observatory for Human Rights said the attacking forces were less than 4 km from Manbij at the closest point. Its director, Rami Abdulrahman, said 56 IS members had been killed so far, and 19 SDF fighters had died.

He said IS group fighters had sent their families out of Manbij, but disputed Darwish's account that IS fighters had also left the city. Darwish said many homes being used by IS members were now empty as they had left with their families. "They took everything they could and left the city," he said.

Reuters could not independently confirm the account.