But with parliamentary polls looming in less than three months, Prime Minister Nuri al-Maliki has taken a hard line.
Despite officials insisting operations against militants, including those affiliated with the Islamic State of Iraq and the Levant (ISIL) jihadist group, are having an impact, the bloodshed has continued unabated.
In and around the capital on Monday, seven car bombs killed 20 people while authorities said they found the dumped bodies of three men and a woman. All were shot in the head and they appear to have been tortured.
Seven people were killed in two separate car bombs -- one of which was detonated by a suicide attacker -- in the town of Mahmudiyah, just south of the capital.
Thirteen others were killed by vehicles rigged with explosives in the Baghdad neighbourhoods of Baladiyat, Hurriyah, Sadr City and Dura.
The killings in particular are a reminder of Iraq's brutal 2006-2007 Sunni-Shiite sectarian war, when corpses were often found abandoned on the streets, with the victims bearing signs of torture.
North of Baghdad in restive Diyala province, separate attacks on security forces left two soldiers dead, while bombings also struck in ethnically mixed Kirkuk province, wounding three people.
January's death toll of more than 1,000 killed nationwide was the highest monthly figure since April 2008, according to government data.
Shootings have largely targeted security forces and civil servants, while bombings have ripped through both Sunni and Shiite areas, striking markets, commercial streets, cafes and other areas where civilians gather.
Ramadi bombs dismantled
No group immediately claimed responsibility for the latest attacks, but Sunni militant groups including ISIL have previously mounted coordinated bombing campaigns in the capital targeting civilians and security forces.
ISIL has also been involved in fighting security forces in Anbar province, a mostly Sunni desert region bordering Syria where militants have for weeks held parts of Ramadi and all of Fallujah, which lies on Baghdad's doorstep.
On Monday, soldiers, police and pro-government armed tribesmen were pressing a joint operation against militant-held areas of Ramadi, with a security official and an AFP journalist reporting that pro-government forces held most of a crucial neighbourhood in the city centre.
Security forces were dismantling dozens of roadside bombs planted across the Malaab district, and were making slow progress in other parts of Ramadi without the advantage of air cover because of bad weather.
On Saturday, the defence ministry announced that bombardment and artillery had hit a neighbourhood of northern Fallujah, a rare military operation inside the city itself.
A security official told AFP that an assault on the city was imminent, but a journalist in Fallujah said it was largely calm on Monday.
The army has largely stayed out of Fallujah, a short drive from Baghdad, fearing major incursions could ignite a protracted conflict with massive civilian casualties and damage to property.
US battles in the city, a bastion of militants following the 2003 US-led invasion, were among their bloodiest since the Vietnam War.
Along with ISIL, other militant groups and anti-government tribes have fought forces loyal to the central government.
The stand-off has prompted more than 140,000 people to flee their homes, the UN refugee agency said, describing it as the worst displacement in Iraq since the peak of the sectarian conflict.