Iraqi premier Haider al-Abadi has "retired" the army's chief of staff, the most senior officer removed since jihadists overran large parts of the country last year, his spokesman said Monday.

General Babaker Zebari "has been retired" on Abadi's orders, Saad al-Hadithi told AFP, without providing further details.

Abadi has sacked dozens of army and police officers in an effort to restructure and improve security forces that performed disastrously when the Islamic State jihadist group launched an offensive last June, overrunning major areas north and west of Baghdad.

But it is unclear if Zebari was removed as part of that effort, or for other reasons.

Multiple Iraqi army divisions collapsed during the initial IS offensive, with soldiers abandoning weapons, vehicles and uniforms in their haste to flee.

The Iraqi military suffers from both poor training -- which the US military says it largely abandoned after the 2011 withdrawal of American forces -- and lacking leadership.

Zebari repeatedly said before the withdrawal that it would be better if American forces stayed, as it would take years for the Iraqi army to be fully ready.

"If I were asked about the withdrawal, I would say to politicians: the US army must stay until the Iraqi army is fully ready in 2020," Zebari told AFP in 2010.

While Zebari was chief of staff, military responsibility was devolved elsewhere post 2011, with former prime minister Nuri al-Maliki centralising control of the armed forces in his office and bypassing the defence ministry.

Three and a half years after US forces left, there are thousands of American soldiers back in Iraq advising and training Baghdad's forces, and the US is leading a campaign of air strikes targeting IS in Iraq and Syria.