DAMASCUS — The U.S.-backed Syrian Democratic Forces pushed into the outskirts of the ISIS stronghold of Manbij in northern Syria on Thursday and were advancing slowly to the center of town, an adviser to the predominantly Kurdish force and a monitoring group said.

The town lies along the only ISIS supply line between the Turkish border and the extremist group’s self-styled capital, Raqqa.

The Britain-based Syrian Observatory for Human Rights said the SDF siezed two squares on the western side of Manbij, then advanced toward a third square with air support from the U.S.-led coalition.

An adviser to the SDF, Nasser Haj Mansour, said troops had moved into the town from its northern edge on Wednesday, close to grain silos, prompting clashes with ISIS militants. He confirmed that other troops entered Manbij from the west.

Journalist Mustafa Bali, who accompanied the SDF fighters on the front line Wednesday, said it was only a matter of time before the silos are taken. They are separated from the city by a main highway, he said, estimating that the SDF are about 1.8 miles from the city center.

The U.S. has embedded 300 Special Forces troops with the SDF. France has also confirmed it is providing training to the SDF.

The Observatory said around 63 SDF fighters and 458 ISIS militants, including field operators and foreign fighters, have died in fighting in the Manbij campaign, which began on May 31. 

The international coalition has since conducted more than 233 airstrikes in the vicinity of the town, according to the command.

ISIS news agency Aamaq said the group’s militants repelled an SDF advance from the town’s north, adding that a suicide attack against the retreating forces killed many fighters.

Mansour, the SDF adviser, said suicide bombings are no obstacle to advancing on Manbij.