Iraq on Tuesday announced the execution of 26 men convicted of "terrorism", including a high-profile anti-Qaeda militia commander whose arrest in 2009 prompted fierce street battles in Baghdad.

The executions come despite widespread international condemnation of Iraq's use of capital punishment, and were announced barely a week after Prime Minister Nuri al-Maliki publicly rebuked Ban Ki-moon over the UN chief's call for a moratorium.

"The justice ministry carried out the executions of 26 (men) convicted of crimes related to terrorism on Sunday," a ministry statement said, adding that all of those put to death were Iraqis.

It said that the ministry would "continue to carry out sentences against those who have been condemned, after the final decision has been made", despite persistent international calls for Iraq to declare a moratorium on its use of capital punishment.

"All 26 who were executed carried out brutal terrorist crimes against the Iraqi people, and they were tried and condemned, and the verdict was approved by the presidency," Justice Minister Hassan al-Shammari said.

Iraq executed at least 169 people last year, according to an AFP tally based on statements from the justice ministry and reports from officials.

It was the highest figure since the US-led invasion of 2003, and placed it third in the world for the number of executions after only China and Iran.

The UN chief urged Iraq to halt executions on a visit to Baghdad this month, but was publicly rebuked by the prime minister who said the country does not "believe that the rights of someone who kills people must be respected."

Among those executed was Adel Mashhadani, who was arrested in March 2009 and sentenced to death in November of that year for killing a young girl in a revenge attack.

Mashhadani headed Sahwa forces in Fadel, one of Baghdad's oldest districts.

The Sahwa, or Awakening, is a Sunni Arab tribal militia that sided with US forces against their co-religionists in Al-Qaeda from late-2006 onwards, a key factor in helping turn the tide of Iraq's insurgency.

A de facto amnesty for the Sahwa in 2008 exempted them for crimes against the state but not crimes against the people.

Mashhadani's arrest in 2009 provoked fierce street fighting in Fadel between security forces and his loyalists.