Story highlights Defense Secretary Ash Carter told CNN's Barbara Starr on "State of the Union" the weak state of Iraq's military is a key reason Ramadi fell to ISIS.

The U.S. has sped up the shipment of some arms to help boost Iraqi forces as ISIS has recently taken more territory.

Washington (CNN) Defense Secretary Ash Carter, in his first comments since the key town of Ramadi fell to ISIS, blamed the weak state of Iraq's military as one major reason for the city's fall, in an exclusive interview on CNN's "State of the Union" aired Sunday.

"What apparently happened was that the Iraqi forces just showed no will to fight," Carter told CNN's Barbara Starr. "They were not outnumbered. In fact, they vastly outnumbered the opposing force, and yet they failed to fight, they withdrew from the site, and that says to me, and I think to most of us, that we have an issue with the will of the Iraqis to fight ISIL and defend themselves."

Carter's remarks are the strongest yet from any Obama administration official speaking on the record since the last week's events when Ramadi fell. The U.S. has sped up the shipment of some arms to help boost Iraqi forces as ISIS has recently taken more territory, but the U.S. defense chief said Iraq's military needs to step up.

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"We can give them training, we can give them equipment -- we obviously can't give them the will to fight," Carter said. "But if we give them training, we give them equipment, and give them support, and give them some time, I hope they will develop the will to fight, because only if they fight can ISIL remain defeated."