The United States has done "nothing" to help Iraq's army battle jihadists in Ramadi, according to a senior Iranian general involved in the fight against the Islamic State group.

Qassem Suleimani, the Revolutionary Guards' commander of foreign operations, hit out at Washington after Pentagon chief Ashton Carter said Iraqi forces "failed to fight" in Ramadi, which has fallen to IS.

"Mr. (Barack) Obama, what is the distance between Ramadi and Al-Asad base where US planes are based?" Suleimani said in a speech late Sunday in the southern province of Kerman carried by state news agency IRNA.

"How can you be in that country under the pretext of protecting the Iraqis and do nothing? This is no more than being an accomplice in a plot," said Suleimani.

Shiite Iran has military advisers in Iraq and Syria and provides financial and military support to the governments of both countries in their battle against Sunni extremists.

According to Iranian media, Suleimani has been active in Iraq, particularly at the end of March when Iran-backed Shiite militias helped to recapture the city of Tikrit.

Ramadi, located about 100 kilometres (60 miles) west of Baghdad, fell to IS on May 17 despite US air strikes and the presence of hundreds of US military advisers at the Al-Asad air base in the same province.

In his remarks on Sunday, Carter said that the US-led air campaign against IS, which controls large swathes of Iraq and Syria, was still working.

He said Iraqi forces had "showed no will to fight" even though they outnumbered their opponents, leading to Baghdad's worst defeat in almost a year.

But Suleimani argued that the United States had "no will to fight Daesh", using an Arabic acronym for IS.

He said the jihadists, who control several oil zones in Iraq and Syria "export their oil via countries belonging to the international coalition" led by Washington.

The struggle against IS was a matter of "national interest", Suleimani said.

On Sunday, General Ahmad-Reza Pourdastan, commander of Iran's ground forces, asked parliament for additional funds to fight the jihadists, who are also present in Pakistan and Afghanistan.