Updated at 1:04 p.m. ET

Iraq and Iran are refuting U.S. Defense Secretary Ash Carter's assertion that Iraqi forces lacked the "will to fight" the self-declared Islamic State, resulting in the loss last week of Anbar Province and its capital, Ramadi.

Saad al-Hadithi, a spokesman for Iraqi Prime Minister Haider al-Abadi, told The Associated Press that Ramadi's loss was due to mismanagement and poor planning by some senior military commanders.

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

In neighboring Iran, Gen. Qassim Soleimani, the head of the elite Quds forces in Iran's Revolutionary Guard, said it was the U.S. that showed "no will" in fighting the Islamic State. He told the daily newspaper Javan that the U.S. didn't do a "damn thing" to stop the extremists' advance on Ramadi.

"Does it mean anything else than being an accomplice in the plot?" he asked, according to the Farsi-language newspaper. His comments were translated by The Associated Press.

Soleimani and other Iranian military officials have been sent as advisers to Shiite militia who are fighting the Islamic State, or ISIS, made up of Sunnis. Iran denies it has troops fighting in Iraq, but several news organizations have reported that Iranian troops are fighting there.

The war of words was sparked by Carter's comments Sunday on CNN's State of the Unionin whichthe defense secretary said though Iraqi forces "vastly outnumber[ed]" ISIS in Anbar, "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."

"We can give them training, we can give them equipment — we obviously can't give them the will to fight," Carter tells CNN.

His comments echoed those made by Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, who said last week that "The [Iraqi Security Forces were] not driven out of Ramadi ... They drove out of Ramadi."

The White House said Monday that Vice President Joe Biden spoke with Abadi and "recognized the enormous sacrifice and bravery of Iraqi forces over the past 18 months in Ramadi and elsewhere."

In an interview last week with The Atlantic, President Obama called the loss of Ramadi a "setback" but denied that the U.S. was losing to the Islamic State.

Obama acknowledged in the interview that the U.S. is going to "have to ramp up not just training" of Iraqi forces in the country's Sunni areas, "but also commitment."

The Associated Press adds:

"Baghdad has said military preparations are underway to launch a large-scale counteroffensive in Anbar province, home to Ramadi, involving Iranian-backed Shiite militias. However, that possibility has sparked fears of potential sectarian violence in the Sunni province, long the scene of protests and criticism against the Shiite-led government in Baghdad.

"Beyond that, Mideast officials gathered this past weekend in Jordan at an economic summit said they wanted more involvement from the U.S. in the Islamic State war, including weapons deliveries and military action beyond its coalition airstrikes. U.S. President Barack Obama and his administration, however, remain leery of involving America in yet another ground war in Iraq after only withdrawing combat troops at the end of 2011."

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