More than a month after it began, the battle for the Syrian city of Manbij drags on.

Now surrounded on all sides by a coalition of Kurds and Arabs, known as the Syrian Democratic Forces, and supported by US Special Operations forces as well as dozens of airstrikes, the assortment of troops is slowly rooting out Islamic State fighters one block at a time.

Yet, despite gains around the city, one cluster of buildings at the southern tip of Manbij has turned into a small redoubt and a symbol of the Islamic State’s determination to hold its territory. The structures, a series of grain silos, elevators, and administrative buildings, have been hit by numerous airstrikes since 2014. And despite various reports of their seizure by the US-backed forces, they still appear either to be partially held by ISIS fighters or so laden with mines and booby traps that advancing troops are unable to enter.

Positioned a little more than a mile from the center of Manbij, the grain silos are a dominating piece of terrain that provides their occupants an unfettered view of the city. For the US-backed Syrian forces, this means that their American advisers would be given an observation tower for calling in airstrikes while their Syrian comrades cleared the rest of the Manbij. The Islamic State knows this and, in turn, has fought doggedly to keep them, littering the buildings with snipers and explosive devices.

Initial reports on social media indicate that Syrian Democratic Forces began fighting around the grain silos in the first five days in June, a little more than a week after the campaign to take Manbij began. As the US-backed forces began to encircle the rest of the city, ISIS refused to budge from the grain towers. It is unclear how many airstrikes have been called in on what appear to be reinforced concrete silos, but pictures and social media reports indicate that they have been continuously hit since the beginning of the month.

‘‘The grain elevators there have been key terrain and offer commanding views of the city and surroundings. It’s definitely a tough fight,’’ said a senior defense official. ISIS “doesn’t want to lose Manbij. The strategic implications are huge for them.’’