Pilgrims attacked
Earlier in the day, 22 people died after an attack in a Sunni district of southern Baghdad, as Shia pilgrims travelled to a religious festival.
Snipers opened fire in the Sunni district of Saydiya, prompting police who were protecting the pilgrims to return fire before a car bomb exploded, killing 12 policemen and 10 civilians.
The blast came as Shia pilgrims streamed through southern Baghdad to the city of Karbala, 80km south of Baghdad.
In another attack on Wednesday, at least five Shia pilgrims were killed and at least 14 wounded after being attacked in Doura.
The attackers exploded a roadside bomb beside the pilgrims and then opened fire on the group.
Security officials also reported that one person died Wednesday when mortar shells hit a group of pilgrims on a road south of Baghdad.
Undaunted
The attack in a mostly Sunni district comes just a day after suicide bombers killed at least 115 Shia pilgrims in the southern city of Hilla.
Despite the rising violence, crowds of pilgrims were out on the streets of Baghdad on Wednesday, seemingly undaunted by the previous day's attacks.
Security in and around Kerbala is tight for fear of a repetition of suicide bombings and attacks on Shia religious rituals by suspected Sunni insurgents of the type that killed 171 people in Baghdad and Kerbala in March 2004.
The attacks on pilgrims this week have occurred just over a year after the bombing of a Shia shrine in the city of Samarra sparked an upsurge in sectarian violence in Iraq.
Baghdad security plan
US military commanders meanwhile pressed ahead with their plan to re-gain control of Baghdad.
In a series of raids conducted across Iraq on Wednesday morning, US forces detained 24 suspected insurgents, the military said.
In a raid northeast of Karmah, 80km west of Baghdad, US troops detained nine suspects they believe have ties to senior al-Qaeda-in-Iraq leaders, the military said in a statement.
In Baghdad, more than 90,000 Iraqi and US troops have intensified operations to rein in violence as part of a last-ditch security plan.
George Bush, the US president, said on Tuesday a new security plan in Baghdad was making gradual progress, despite the killing of nine US soldiers north of the capital in two separate bomb attacks the day before.
More than 3,185 American soldiers have died in Iraq since the US-led invasion in March 2003.