Iraq and Iran pushed back Monday against U.S. Defence Secretary Ash Carter's criticisms over the fall of Ramadi to the Islamic State in Iraq and Syria, with an Iranian general going as far as saying America had "no will" to fight the extremists.

In Baghdad, a spokesman for Iraq's prime minister suggested Carter had "incorrect information," while Gen. Qassim Soleimani, the head of the elite Quds forces in Iran's Revolutionary Guard, offered his own assessment of American forces.

The war of words over the loss of Ramadi, amid other gains by ISIS, lay bare the fissures among countries that have become allies of convenience against the militants. And as Iraqi troops continue to flee their advance, governments across the world are questioning whether relying on Iraqi troops and militiamen on the ground alone will be enough to stop them.

The criticism began Sunday, when Carter told CNN's State of the Union news show that Iraqi forces "vastly outnumbered" ISIS militants, but still "showed no will to fight" and fled their advance on Ramadi.

On Monday, Saad al-Hadithi, a spokesman for Iraqi Prime Minister Haider al-Abadi, said his government was surprised by Carter's comments.

"Carter was likely given incorrect information because the situation on ground is different," al-Hadithi told The Associated Press. "We should not judge the whole army based on one incident."

Didn't do a 'damn thing'

Al-Hadithi said the Iraqi government believes the fall of Ramadi was due to mismanagement and poor planning by some senior military commanders in charge. However, he did not elaborate, nor has any action been taken against those commanders.

In Iran, the daily newspaper Javan, which is seen as close to the Revolutionary Guard, quoted Soleimani as saying the U.S. didn't do a "damn thing" to stop the extremists' advance on Ramadi.

Gen. Qassim Soleimani, the head of the elite Quds forces in Iran's Revolutionary Guard, accused the U.S. of having 'no will' in fighting ISIS. (Office of the Iranian Supreme Leader via Associated Press)

"Does it mean anything else than being an accomplice in the plot?" he reportedly asked, later saying the U.S. showed "no will" in fighting ISIS.

Soleimani said Iran and its allies are the only forces that can deal with the threat.

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

American Vice-President Joe Biden reassured Iraq's government of U.S. support in the fight against ISIS in a telephone call to Prime Minister Haider Al-Abadi on Monday.

A White House statement described Biden's call as recognizing "the enormous sacrifice and bravery" that Iraqi forces had displayed over the past 18 months in Ramadi and elsewhere.

The White House also said Biden welcomed an Iraqi decision to mobilize additional troops and prepare for counter-attack operations.

U.S. Vice-President Joe Biden reassured Iraq's government of U.S. support in the fight against ISIS in a telephone call Monday. (Matt Rourke/Associated Press)

U.S. officials, including Carter, have said Iraqi forces fled the ISIS advance on Ramadi without fighting back, leaving behind weapons and vehicles for the extremists. So far, the American approach to the conflict has been to launch airstrikes as part of an international coalition it leads, as well as equipping and training Iraqi forces.

Iran has offered advisers, including Soleimani, to direct Shia militias fighting against the extremists. Iran has said it does not have combat troops fighting in Iraq, though some Revolutionary Guard members have been killed there.

Leery of new ground war

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

At least 15 killed in air raids

Meanwhile in Syria, government warplanes conducted more than 15 air raids on the ISIS-held town of Palmyra and nearby areas, leaving some dead or wounded. The air raids on Palmyra came a day after the government said that ISIS fighters have killed more than 400 state employees, soldiers and pro-government gunmen since they captured the town Wednesday.

The airs raids also came two days after the U.S.-led coalition struck ISIS positions near Palmyra.

The Britain-based Syrian Observatory for Human Rights and Osama al-Khatib, an activist from Palmyra who is now in Turkey, said the air raids were mostly inside the town and about two kilometres from the famous archaeological sites that are among the Middle East's most spectacular.

Syrian state TV, quoting a military official, said government warplanes destroyed ISIS "hideouts" in Palmyra and nearby areas, killing and wounding an unspecified number of ISIS fighters.

Khaled al-Homsi, an activist inside Palmyra, said the air raids mostly hit homes of civilians. He said at least 20 people were killed and dozens injured while al-Khatib said at least 15 were killed.