The government has failed to curb a year-long surge in violence that has reached levels not seen since 2008, when the country was just emerging from a brutal period of sectarian killings in which tens of thousands died.
In the deadliest attack today, an explosives-rigged motorcycle ripped through an area of motorcycle shops in the Shiite-majority Sadr City district of Baghdad, killing at least 27 people and wounding 40, the interior ministry said.
Sunni extremists frequently target members of Iraq's Shiite majority, who they consider apostates.
The capital is hit by near-daily bombings and shootings, including periodic coordinated vehicle bomb attacks that leave dozens of people dead.
In Mishahada, north of Baghdad, a car bomb exploded near an army patrol, killing at least two soldiers and wounding three.
Other attacks hit areas in northern Iraq.
A roadside bomb exploded near a Sahwa anti-Al-Qaeda militia patrol in the Sharqat area, killing two fighters and wounding four, while a roadside bomb near a police station in Tuz Khurmatu killed two people and wounded 15.
The latest violence came as Maliki accused foreign states of backing a powerful jihadist group, the Islamic State of Iraq and the Levant in Iraq.
"Some states do not want ISIL, especially on their territory, but they want ISIL in Iraq" for "sectarian" reasons, Maliki said in an interview broadcast on Iraqiya state television.
"We know the details of ISIL and its foreign ties and the ties of states to it, and the funding that comes to it," Maliki said.
The premier was apparently referring to Sunni-majority Gulf states including Saudi Arabia, Iraq's southern neighbour.
