The "final battle" with ISIS is in its final days, with ISIS is pinned down to an area of around a quarter of a square mile. That's the update reporters received Saturday from the commander of the U.S.-backed Syrian Democratic Forces, Jia Furat.

He said the final ISIS village of Baghuz Fawqani had not yet fallen, but his ground forces were holding fire and moving forward cautiously because so many civilians remain trapped as human shields.

Military officials say they severely underestimated the number of civilians inside that village when they launched the offensive to crush the last remnants of the so-called caliphate one week ago.

Furat estimated to be around 1,500 people, more than twice that many have since flooded out this week, including many ISIS families.

Hundreds of ISIS fighters reportedly surrendered this week, of the approximately 450 militants who were thought to be making a last stand.

When CBS News visited the frontline on Thursday, we found SDF fighters on a more relaxed footing since the final offensive began, and apart from sporadic gunfire, a relative calm suggested that the brutal last battle might be coming to an end.

Furat on Saturday vowed to "broadcast to the world in the coming days the military end of ISIS."

Furat specified "military end," because even us-led coalition officials have said the terror group will remain a threat as an underground insurgency – which raises important questions about when america's 2.000 troops will withdraw.