Iraq and Iran refuted U.S. Defense Secretary Ash Carter's claims that Iraq's military lacked the "will to fight" the Islamic State group, which he said led to the loss last week of Anbar Province and its capital city of Ramadi.

Carter told CNN's "State of the Union" on Sunday: "What apparently happened is the Iraqi forces just showed no will to fight. They were not outnumbered; in fact, they vastly outnumbered the opposing force. 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."

But Saad al-Hadithi, a spokesman for Iraq's prime minister, told The Associated Press on Monday that Carter had "incorrect information," and that Ramadi's loss was actually due to mismanagement and poor planning by senior military commanders.

"Carter was likely given incorrect information because the situation on the ground is different," he told AP. "We should not judge the whole army based on one incident."

In Iran, the Javan daily newspaper quoted Gen. Qassim Soleimani, the head of the elite Quds forces in Iran's Revolutionary Guard, as saying it was the U.S. who didn't do a "damn thing" to stop the Islamic State group from taking over Ramadi, according to AP.

"Does it mean anything else than being an accomplice in the plot"? he asked, adding that the U.S. showed "no will" to fight the extremist group.

Iran and its allies are the only forces capable of dealing with the Islamic State group, Soleimani said.

"Today, there is nobody in confrontation with (the Islamic State group) except the Islamic Republic of Iran, as well as nations who are next to Iran or supported by Iran," he said, according to AP.

Soleimani, known in Western media as the "Shadow Commander" and "Dark Knight," has reportedly been sent along with other military officials to advise Shiite militia who are fighting the Islamic State group in Iraq. Iran denies it has sent combat troops to the area, but some Revolutionary Guard members have been killed there, as reported by various media outlets.

The Iranian-backed Shiite militias are working alongside the U.S.-trained Iraqi forces to take back key cities, and reportedly key to the Iraqi government's plan to take back Ramadi.

Col. Peter Mansoor, who served as the executive officer for Gen. David Petraeus in Iraq, told the Christian Science Monitor, "Quite frankly, Soleimani is correct."

"The shortfalls in our strategy are becoming apparent: Shiite militias are a more capable ground force now because they have Iranian advisers embedded in them," he added. "The Shiite militias are commanded by committed leaders, and the weak ones are being weeded out. You can't say the same thing about the Iraqi Army."