"According to a judicial decision, 10 'terrorists' of the group led by Sheikh Zhana Abdel Karim Barzanzi were executed today in Arbil," a security official said on Thursday.
Barzanzi, a Kurdish graduate in mechanical engineering, was one of the 10 who were convicted in March of leading a cell linked to the Islamist group Ansar al-Sunna.
The official said that during their interrogation the group had admitted to beheading people and carrying out bomb attacks in Arbil and Dohuk.
In Baghdad, meanwhile, six policemen were killed when their station was hit with mortar and gunfire, also on Thursday.
Nearly 2,000 Italian troops are
stationed in Dhi Qar province
In a separate incident, the US military said an American soldier was killed by a roadside bomb in the capital.
In other scattered violence around Baghdad, four civilians were killed and five wounded in a mortar attack on a residential area in the Dora neighbourhood in the city's south.
Two civilians were killed and six more injured when a parked car bomb exploded in the northeast.
Two more people were killed and another nine injured when a car bomb exploded near an electricity office in the capital.
In Baqouba, 60km northeast of Baghdad, a policeman was killed and another wounded when a police car was fired upon by unknown assailants.
In the northeastern Diyala province, a convoy was hit by a roadside bomb attack, injuring the governor's brother and three guards. The governor was not in the convoy.
In Falluja, 65km west of Baghdad, parts of two mutilated bodies were found.
A joint US and Iraqi patrol clashed with forces loyal to radical Shia cleric Muqtada al-Sadr in al-Diwaniyah, 130km south of Baghdad, in a raid to arrest a Mahdi Army leader.
An Iraqi armoured personnel vehicle and a US Humvee were damaged, but there were no immediate reports of American casualties.
It was not confirmed whether there were any Mahdi Army fighter dead or wounded.
Iraq has taken control of security from Italian and Romanian troops in the largely Shia southern province of Dhi Qar, paving the way for the coalition forces to leave.
We will continue to receive control of other provinces as we manage to get our country back from the hands of the Baath dictatorship
Nuri al-Maliki, Iraq's prime minister
The relatively peaceful province is the second of the country's 18 provinces to be handed over to Iraqi forces by the US-led coalition after the July transfer of power in Al-Muthanna province.
Prior to Thursday's handover, 1,860 Italian and 430 Romanian troops were in charge of security in Dhi Qar.
During a handover ceremony, Nuri al-Maliki, Iraq's prime minister said: "We will continue to receive control of other provinces as we manage to get our country back from the hands of the Baath dictatorship (in a reference to the regime of Saddam Hussein).
"We still have to improve basic services. There are those who work to support terrorists. We tell them that those days are gone."