Militants carried out bombings and shootings in 10 cities and towns in Iraq on Sunday, killing at least 33 people and wounding 106, in the latest wave of deadly attacks to hit the country.

In total, at least 253 people have been killed and 803 wounded in attacks in Iraq this month, according to an AFP tally based on security and medical sources.

Insurgents are regarded as weaker than when violence reached its peak in 2006 and 2007 but they remain able to carry out spectacular mass-casualty attacks and have shown they can strike heavily-guarded sites such as prisons and police stations.

Most of Sunday's attacks were centred in Baghdad and the nearby areas of Taji, Madain and Tarmiyah, where an interior ministry official said 25 people were killed and 59 wounded. Medical sources put the toll at 28 dead and 77 wounded.

In Baghdad, a suicide bomber detonated an explosives-packed car in the central Karrada district, targeting the deputy head of police for the area, a police officer at the scene said.

The explosion scattered debris for dozens of metres (yards) from the site of the blast, shattered store windows and smashed cars. A headless, limbless torso surrounded by pieces of flesh lay at the scene.

Police, most of them armed with Kalashnikov assault rifles, deployed in force on the street, and a fire truck sprayed down the blast site.

"We were working and we heard a loud explosion, and the air changed and everything exploded," said Firas Dawood, the owner of a nearby shop.

"What do I say about the security measures? Shit," he said.

"We are tired of this government," said Haidar Mohammed, an employee of a shop on the street hit by the blast. "The government does not do anything."

"I was in my shop and I heard the sound of a very powerful explosion," said another store owner who gave his name only as Abu Ihab. "Dust was everywhere."

"We were sitting in the shop while police were collecting flesh," he said. "Human flesh was on the sidewalk, being collected and put in plastic bags."

"When the explosion happens, it does not care about any security measures," he said. "I sit in my shop and I am afraid for my life."

Abu Ihab soon had another reason to be afraid, as the blast was followed by a second car bomb that hit the same area.

Gunmen also shot dead a policeman in the Al-Amil neighbourhood of south Baghdad, an attack followed by a car bomb that exploded after a police patrol came to investigate, the interior ministry official said.

And a police colonel was wounded by gunmen in the Mansur area of west Baghdad, the ministry official and a medical source said.

North of the capital, four car bombs exploded in Taji.

The first went off near a Shiite place of worship, followed by three others in the same Al-Askari neighbourhood of the town, a security official said, adding that women and children were among the dead.

In Madain, south of Baghdad, a car bomb exploded near a bus carrying Iranian pilgrims, a witness said.

And two roadside bombs targeted army and police patrols in the Tarmiyah area, north of Baghdad.

A car bomb targeting a police convoy killed two policemen and wounded seven others near Baquba, north of Baghdad, while another car bomb exploded south of Baquba, killing one person and wounding seven, police and a doctor from Baquba General Hospital said.

North of Baquba, a car bomb targeting police Brigadier General Mohammed al-Tamimi wounded five people, a police colonel and the doctor said.

South of Baghdad, in Kut, a car bomb exploded near a police river patrol station, killing a civilian and three police, and wounding seven people, a police captain and a medical official said.

In the main northern city of Mosul, a car bomb exploded near an army patrol, wounding 15 people, among them a soldier, while a roadside bomb wounded four policemen, doctors and police said.

And an explosives-rigged vehicle exploded near an army patrol south of the northern oil city of Kirkuk, killing a soldier and wounding a civilian and another soldier, police and a doctor said.

South of Baghdad, police arrested two people as they attempted to drive explosives-packed vehicles into the city of Diwaniyah, provincial police chief Brigadier General Abdul Jalil al-Assadi said.