A coordinated string of bombings and a brazen assault on a ministry near Baghdad's heavily fortified Green Zone have killed 18 people, adding to the 120,000 Iraq war victims tallied in a new study.

The conflict has cost the lives of at least 116,000 Iraqi civilians and more than 4,800 coalition troops between the outbreak of war in 2003 and the US withdrawal in 2011, US researchers estimated on Friday.

Thursday's attacks, which drew condemnation from the US, UN and Iraq's parliament speaker, come just days before the 10th anniversary of the US-led invasion, and with barely a month to go before the country holds its first elections in three years.

No group immediately claimed responsibility for the violence, but Sunni militants including those linked to Al-Qaeda often target government officials and offices in a bid to destabilise Iraq.

At least three bombs exploded in Allawi neighbourhood, near the foreign and culture ministries and offices of the communications ministry, at about 1:30 pm, officials and witnesses said.

At around the same time, militants staged an apparently unsuccessful assault on the nearby justice ministry.

Overall, 18 people were killed and at least 30 wounded in the attacks, an interior ministry official and a medical source said.

All of the buildings lie near the Green Zone complex in central Baghdad, home to parliament, the prime minister's office and the US and British embassies.

"Some terrorists tried to infiltrate the justice ministry," said Sabah Noori, spokesman for Iraq's Counter-Terrorism Service.

"The bombs... were coordinated with them (militants) trying to get into the ministry."

Gunfire was heard after the blasts, and smoke could be seen rising above the neighbourhood, witnesses said.

Security forces sought to bar the press from taking photos or video, according to an AFP journalist.

Accounts differed on how successful the militants were in their assault on the ministry.

An official in Baghdad's security command centre said three fighters were killed inside the justice ministry building, but ministry spokesman Haidar al-Saadi said clashes had occurred only outside.

An interior ministry official, however, said two fighters were killed in clashes while two others were suicide bombers who blew themselves up, one of whom did so near the justice minister's office.

Saadi said no ministry employees were hurt, and Iraqiya state television reported that security forces evacuated all employees from the building.

A justice ministry employee told AFP that staff escaped from the building via a rear entrance, and reported clashes between militants and security forces in which fighters used hand grenades.

Though such coordinated assaults are rare, Iraq has been struck by them in previous years -- several ministries, police stations, prisons and provincial council offices have been hit by a combination of bombings followed by assaults in which militants tried to wrest control of official buildings.

The United States' involvement in Iraq has so far cost it $810 billion (625 billion euros) and could eventually reach $3 trillion, according to estimates from two US professors of public health, reporting in the British peer-reviewed journal The Lancet.

Professors Barry Levy and Victor Sidel base the figures, and the death tolls, on published studies in journals and on reports by government agencies, international organisations and the news media.

"We conclude that at least 116,903 Iraqi non-combatants and more than 4,800 coalition military personnel died over the eight-year course" of the war from 2003 to 2011, they said.

"Many Iraqi civilians were injured or became ill because of damage to the health-supporting infrastructure of the country, and about five million were displaced.

"More than 31,000 US military personnel were injured and a substantial percentage of those deployed suffered post-traumatic stress disorder, traumatic brain injury, and other neuropsychological disorders and their concomitant psychosocial problems."

Also on Thursday, a bombing targeted a candidate in Iraq's upcoming provincial elections, who escaped unhurt, after another was kidnapped along with his father and other relatives north of Baghdad the night before.

Provincial elections are to be held on April 20, Iraq's first vote since March 2010 parliamentary polls.