Dozens of people were killed and injured in two attacks that rocked Iraq on Saturday.

At least 37 people were killed in a car-bomb attack on a packed bus station near one of Iraq's holiest shrines in Karbala, about 70 kilometres south of Baghdad.

Separately, in an attack in Baghdad, 10 people were killed when a car bomb targeted a key bridge in the capital's downtown -- the second such strike on the site this week.

At least 15 people were wounded in the bombing on the Jadriyeh bridge over the Tigris river. The structure suffered little damage, The Associated Press reports.

The bus station that was attacked lies roughly 200 metres from the Imam Hussein shrine in Karbala. The site -- an important location for Shiites -- is the final resting place of the grandson of the Prophet Muhammad.

After the bombing -- which wounded more than 70 people -- state television aired images of rescue workers hauling charred bodies from the scene.

At least six children were among those killed, according to an official at Al-Hussein Hospital.

"I want my father. Where is my father?" cried out 11-year-old Sajad Kadhim as he lay in the grounds of the hospital, where doctors were treating his burns.

"All I remember was we were shopping. My father was holding my hand and suddenly there was a big explosion. I don't know where my father is. I want my father," the boy cried.

Others frantically searched through the hospital for their missing children.

In the chaos that followed the attack, hundreds of angry and upset people swarmed emergency service vehicles. Police fired into the air to try and disperse the crowds, triggering a riot. Angry mobs attacked the officers and set fire to two police vehicles.

Demonstrators then surrounded the Karbala governor's office, demanding the resignation of the governor and other provincial politicians who they said were responsible for the lack of security. The mobs threw stones at the office and set the building on fire.

Hilary Brown, of ABC News, told CTV Newsnet the attack so close to a key Shiite shrine serves as a victory for the insurgents.

"All insurgents, whether they are the secular Sunni insurgents or the Al Qaeda in Iraq -- the more fanatical Sunnis -- they are fighting a battle of perception and they aim to hit symbolic targets with religious or sectarian significance. They see that as critical to their success," she said from Iraq.

The Karbala attack triggered a security crackdown, with the city's entrances sealed off and police and soldiers patrolling the streets.

Brown said the holy site has seen worse attacks in the past. In 2004, a series of bombings on the mosque left 200 people dead, she said, suggesting Iraqis are getting used to the constant loss of life.

"I think generally the Iraqi population after four years of this and an estimated 600,000 civilian deaths according to one respected study, perhaps they are getting slightly desensitized to it."

With files from The Associated Press