Prime Minister Tony Abbott has confirmed that the 200-strong Australian Special Operations Task Group in Iraq has begun providing "training and assistance" for the Iraqi Counter-Terrorism Service (CTS) in its battle against Islamic State.

Military experts regard the service as the most capable and resilient element of the Iraqi security forces. However, former Australian defence intelligence officers say the service has "unquestionably been responsible for major war crimes and unnecessary civilian casualties".

Created and trained by the United States military to hunt down al-Qaeda in Iraq (AQI) militants, the service is directly responsible to Iraqi Prime Minister Haider al-Abadi and operates independently from the Iraqi defence and interior ministries.

The CTS grew rapidly under former Iraqi prime minister Nouri al-Maliki, from 1500 personnel in 2007 to more than 12,000 in early 2014. Two brigades of the Iraqi Special Operations Force (ISOF) provide the CTS's primary combat capability.

Lieutenant-Colonel Jan Gleiman, a US Army officer and visiting fellow at the Australian Strategic Policy Institute, describes the ISOF as "probably Iraq's most trusted and capable military unit".

"When Iraqi army units disintegrated en masse [in mid-2014], the ISOF brigades held together and were forced to do much of the fighting. As a result, they've suffered a very high attrition rate and by some accounts are at 50 per cent of their former strength."

Combat against IS also saw ISOF units involved in summary executions of suspected militants.

In March 2014, Reuters reported that a senior general in Baghdad acknowledged that CTS units had executed prisoners, justifying such behaviour as "a field reaction" to IS atrocities.

"Usually, this happens when there is a military confrontation. The soldiers are finishing off the wounded militants, shooting them many times to express their anger," he said.

Iraqi special forces soldiers openly discussed executing suspected militants, posted pictures on social media accounts, saying "after we kill them, then we plant the weapon by his side".

"Whoever we capture now as a terrorist, we kill him on the spot except for someone we want to investigate," one soldier told Reuters. "I've watched dozens executed."

A US diplomatic cable published by WikiLeaks shows US General David Petraeus told Mr Maliki in November 2009 that the Iraqi special forces were "the most important forces in the counterterrorism fight".

General Petraeus expressed concern that the Iraqi judiciary were too slow to issue warrants for the CTS to arrest terrorist suspects.  Other US military documents published by WikiLeaks show this problem was remedied by securing warrants after arrests had been made and sometimes after suspects had been killed.

The CTS came under control of the prime minister during the administration of Mr Maliki, who was widely criticised for his strongly sectarian Shiite rule.

Many of the service's officers have trained in the United States. However the US State Department had to insist on extra time for visa processing in order to weed out personnel responsible for "gross violations of human rights".

In 2011, Human Rights Watch reported that CTS held detainees in secret jails, torturing and committing other abuses against them. According to Human Rights Watch Middle East director Sarah Leah Whitson, alleged abuses included beatings, applying electric shocks, repeated partial asphyxiation with plastic bags and suspension by the ankles.

In November 2012, US President Barack Obama transferred responsibility for supporting the CTS from the US Defence Department to the Central Intelligence Agency, which has been recently recruiting civilian "security assistance mentors and advisors" to work with the Iraqi service.

"The CTS delivered results in operations against AQI, but it was at the expense of the rule of law, and of building the rest of the Iraqi security forces, which collapsed in the face of ISIL," a former Australian Defence intelligence analyst told Fairfax Media.

The Defence Department says Australian Defence Force personnel are required to report any evidence of human rights violations.

"No instances of alleged human rights violations have been reported since the Special Operations Task Group started co-operating with the Iraqi Counter-Terrorism Service in late 2014," a Defence Department spokesperson said.

Fairfax Media has asked who commands the Iraqi special forces with whom the Australians are working. Defence said that the Australian forces are working with the Counter-Terrorism Academy, commanded by a General Fallah, and the Counter-Terrorism Training unit, directed by a General Omar.