At least 15 people were also wounded when the bomber, riding a motorcycle, blew himself up in the capital’s central al-Andalus Square on Tuesday.
A party official said none of the dead were communists.
In other violence, fighters destroyed a police station south of Baghdad in a sustained attack with mortars and a car bomb according to the prime minister’s office.
The assault, which took place on Monday, was launched with the detonation of a car bomb near the police post in Jorf al-Sakhr, 60km south of Baghdad.
Three police officers were killed and several more people were wounded, including eight US soldiers on the site, according to the US military.
The station had been operational for only two weeks and had cost nearly $500,000 to build and opened in a joint US-Iraqi ceremony.
In the nearby town of Mahmudiya, five more civilians were killed by a pair of bombs that exploded near an Iraqi army base.
Another roadside bomb in nearby Latifiya, went off next to a truck belonging to the finance ministry. One man was killed and five wounded.
In the central Baghdad neighbourhood of Zayuna a car bomb exploded, wounding three people and was followed by a second explosion that hit the crowd of bystanders alerted by the first blast.
Two civilians were killed in that blast and 23 others, including eight policemen, were wounded.
Clashes between armed groups in the southwest Baghdad neighbourhood of Amil resulted in three deaths and 10 wounded, according to police.
The armed groups eventually retreated after setting fire to a number of shops in the nearby Bayaa neighbourhood.
Further north, the pipeline shipping crude oil from the fields around Kirkuk to the refinery in Baiji was blown up, apparently by mortar attacks.
The city itself was also hit by three blasts that killed three civilians and wounded seven.
Amid the violence, the country’s politicians took tentative steps to resolving the issue of autonomous regions.
The subject has split parliamentarians along sectarian lines and on Tuesday parliament named a committee to draft amendments to the constitution, a Sunni demand, and read out a bill to allow for regional autonomy, a key demand of powerful Shia leaders.