US vice-president Joe Biden on Monday spoke to the Iraqi prime minister, Haider al-Abadi, to reassure him of US support, a day after controversial remarks by the defense secretary, Ash Carter, sparked an argument over the recent military successes of Islamic State.

Carter told CNN on Saturday Iraqi forces had shown “no will to fight” Isis and had fled in Ramadi despite outnumbering the militants. Isis also captured Palmyra, in Syria, last week.

A spokesman for Abadi subsequently told the Associated Press Carter had been given “incorrect information”, and said: “We should not judge the whole army based on one incident.”

A White House statement on Monday said Biden recognised “the enormous sacrifice and bravery” that Iraqi forces had displayed over the past 18 months in Ramadi and elsewhere, and welcomed an Iraqi decision to mobilise additional troops and prepare for counterattack operations.

Nonetheless, rival powers and allies traded barbs and accusations over the recent successes of Isis, amid warnings that it may execute hundreds of hostages captured in its latest battles.

In Iran, Qassem Suleimani, the commander of the Quds Force, the external operations arm of the Revolutionary Guards, said the US had “no will” to fight Isis.

“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,” Suleimani told a daily newspaper, Javan, on Monday.

Suleimani said US fighter jets had done nothing to halt the Isis advance on Ramadi, and said the US was complicit in the group’s expansion.

On Monday, the most senior British military officer to be involved in postwar planning in Iraq, Major General Tim Cross, said the Iraqi army lacked the necessary “moral cohesion” to fight against Isis.

In Washington, Republican attacks on the Obama administration over its policy against Isis have grown louder. On Sunday John McCain, the chair of the Senate armed services committee, mocked President Obama for saying climate change was a threat to US national security when advances by Isis had not been checked.

The international war of words highlighted disagreements between the US, Iraq and Iran over how to combat Isis. Months of air strikes have failed to check its advances.

Last week, the militant group seized the capital of the predominantly Sunni Anbar province, its greatest victory in Iraq since its conquest of Mosul last summer and its declaration of a caliphate spanning swaths of Iraq and Syria.

Isis advances have not been limited to Iraq. Last week, the group took control of the historic Syrian city of Palmyra and strategic gas fields nearby after a week-long siege that routed forces loyal to President Bashar al-Assad. The victory has triggered a humanitarian crisis, due to the flight of thousands of residents.

Isis has so far executed more than 200 people in the city and nearby villages, including civilians as well as pro-Assad fighters, according to the Syrian Observatory for Human Rights, a UK-based monitoring group with wide contacts in Syria.

The group also holds some 600 captives from its battles in the east of the city of Homs and Palmyra, including pro-government fighters and civilians it accuses of aiding Assad. They are likely to face the same fate.

The Assad regime said Isis had killed 400 civilians in Palmyra over the weekend, a claim both unsupported and contradictory to the regime’s own declaration when it withdrew from Palmyra that it had evacuated most of the civilians in the city.

Assad’s air force launched more than a dozen air strikes on Palmyra on Monday, including raids near the ancient ruins of the city, which many fear Isis might damage or destroy.