The Syrian Democratic Forces (SDF) are on the northern edge of Manbij, a strategically important town held by ISIS forces that serves as a waypoint between Raqa and the Turkish border.
"At the pace they're moving now and at the speed that they've been able to fight the enemy, we think they're a matter of days before they conduct the attack on (Manbij)," Baghdad-based military spokesman Colonel Chris Garver told Pentagon reporters in a video call yesterday.
The Arab-Kurdish offensive on Manbij is one of two major assaults on the route the ISIS group uses to send in more fighters, weapons and money from the Turkish border to Raqa.
Tabqa, another ISIS-held transit town which lies near Syria's largest dam, is also under attack.
Russian-backed regime forces are also attacking ISIS jihadists in the region and the proximity of Russian- and US-backed forces has led observers to question whether the two powers are coordinating over an eventual assault on Raqa.
"There is no coordination between us and those (Russian-backed) forces at this time," Garver said.
"The forces we support are focused on Manbij right now, and that's where we're supporting them."
Washington, which has more than 200 special forces troops deployed to back the SDF, has said some 3,000 Arab fighters are taking part in the assault, supported by about 500 Kurds.
But the Syrian Observatory for Human Rights says that of the 4,000 fighters it estimates are taking part, most are actually Kurdish.
Garver said "anywhere upwards of a couple thousand" ISIS fighters are in Manbij.
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