Aljazeera's correspondent in Arbil,
Ahmad al-Zawiti, said guards opened fire at the explosive-laden car as it entered the centre on Monday.
However, the driver managed to enter and blow up the car inside, killing at least 13 people and injuring more than 107 others, the correspondent reported.
Some of the injured were discharged from hospital, he said.
About 70 others are still receiving medical treatment there, he added.
Medical sources in Arbil hospitals have confirmed that the injured are in stable conditions, ruling out an increase in the toll.
The correspondent confirmed that all those killed were newly-appointed traffic police officers.
The attack occurred on a main street that leads to the oil-rich northern Iraqi city of Kirkuk, which is south of Arbil, police said.
Police station attacked
Also on Monday, fighters detonated a car bomb and fired on Iraqi police and soldiers in Baghdad, killing at least five Iraqi security force members and wounding nearly 20, the US military said.
The clashes happened shortly after US troops came under attack from armed men near a police station in the Baya district of southwest Baghdad before dawn.
An Iraqi police car lies burnt out
in the Baya district of Baghdad
"When an Iraqi police patrol responded to the incident, terrorists detonated a vehicle-borne improvised explosive device, killing four police and wounding four others," the US army said, using the term for a car bomb.
Police and hospital officials say at least eight police officers and one baby were killed in the attack, and at least 23 people were wounded.
Police Captain Talib Thamir said the attack on the Baya police station began just before dawn and included at least three car bombs, rocket-propelled grenades and small arms fire.
An eight-month-old baby was killed in the attack and a police major-general was among the wounded, Thamir and Dr Muhaned Jawad of Yarmuk hospital said. At least five police vehicles were destroyed, Thamir added.
A bomber attacked a restaurant
on Sunday, killing 23 people
US soldiers repelled the attack, said Sergeant 1st Class David Abrams, a spokesman for Task Force Baghdad.
At least one Iraqi police officer was missing. No US casualties have been reported.
Reuters Television pictures showed a column of smoke rising from near a building in the area, as a US helicopter circled low overhead and occasional shots of gunfire rang out.
Over the past seven weeks, more than 1000 Iraqis, including many police and soldiers, have been killed in a blitz of bomb and gun attacks throughout the country.
US soldier killed
A US soldier was killed early on Monday after a homemade bomb attack against his patrol near the northern Iraqi town of Tal Afar, a US military statement said.
Details of the attack were withheld pending notification of the victim's relatives.