Another bomb was thrown into the garden of a building used by Sunni scholars, including poll candidates, in Mansour in west Baghdad, wounding two guards.
A third blast damaged the headquarters of the United Iraq list in east Baghdad.
Another blast wounded two people when it struck the headquarters of the Moderate Movement list in Karrada in east Baghdad and one other person was hurt when a bomb struck a building used by an election list led by Nehru Abdulkarim al-Keznazani.
The blasts follow the release of an audio recording by Omar al-Baghdadi, the purported leader of al-Qaeda in Iraq, in which he threatened to foil the elections.
In a statement posted on the internet on Friday, al-Baghdadi said: "Sunni participation in this election will certainly lead to the establishment of the principle that Sunnis in Iraq are a minority who have to be ruled by the rejectionists."
The term "rejectionists" refers to the country's majority Shias, which al-Qaeda in Iraq sees as heretical.
In the recording he said this had prompted his group to attempt to "prevent these elections" using "primarily military means".
The recording could not be independently confirmed, but the US-based SITE Intelligence Group that monitors such websites said the voice seemed like that of the person previously identified as al-Baghdadi.
Saturday's blasts feed into Iraq's election turmoil, already strained by the back-and-forth over the ban on candidates accused of ties to the outlawed Baath party of Saddam Hussein, the former Iraqi president ousted by the US-led invasion in 2003.
US officials are deeply concerned the ban could threaten Iraq's political stability ahead of the withdrawal of American combat troops by the end of August.
The ban, which blacklisted more than 500 candidates, among them both Sunni and Shia, has most severely affected the Iraqiya list.
A spokesman for the group said it was unclear how many of the coalition's candidates had been banned from running, but said election officials initially put the number at 72.
Al-Mutlaq, who is among the banned candidates from Iraqiya, has been strongly critical of Nuri al-Maliki, Iraq's Shia prime minister.
A panel confirmed the ban on al-Mutlaq - who has acknowledged he was a Baathist until the late 1970s when he quit the party - earlier this week.
All but 177 candidates have dropped out or been replaced by their parties.
The appeals panel has only cleared 26 names on the blacklist, according to Faraj al-Haidari, the head of Iraq's election commission.