On Wednesday, a car bomb exploded in a busy market near the Shia al-Kamaliyah mosque in east Baghdad. At least 10 civilians were killed, with another 26 wounded.
Two more car bombs later detonated near the Sunni al-Samuri mosque, killing at least five people and wounding at least 10.
A policeman was killed by a bomb attack elsewhere in the province, while mortars hit a house in the nearby town of Hawija, killing a mother and two of her children.
Eight people were killed in attacks across the country, including five in Baquba, capital of the Diyala province.
Two suicide car bombs also hit the headquarters of the Iraqi army's 2nd Battalion near the city of Kirkuk, killing four soldiers and wounding 10.
As the attacks continued, Muwaffaq al-Rubaie, al-Maliki's national security adviser, said the new security plan involved a swifter transition from US troops to Iraqi forces.
He said US forces would move to the outskirts of Iraqi cities to combat al-Qaeda fighters, while Iraqi forces would be charged with dealing with sectarian conflict in Baghdad.
"The coalition forces should not get involved in sectarian violence - this is a job for the Iraqi security forces to do," he told CNN.
On Tuesday, the White House said George Bush, the US president, would detail a new Iraq strategy in January.
Al-Rubaie's announcement indicates changes may already be under way.
Major General William Caldwell, a US spokesman, said US forces would remain as advisers with Iraqi forces to train them and ensure they remain neutral.
He said: "Their real purpose is to provide leadership, mentoring and coaching, but they in fact will be able to observe what we call professionalism to make sure [the Iraqis] are not acting in a sectarian manner out there."
Caldwell said more effort was needed by Iraqi political leaders to stem the violence.
"Until that political process gets more engaged and the political leadership and the political parties become more concerned about this than anyone else, we are not going to see a turn in the levels of violence," he said.
Al-Maliki has promised to hold a national reconciliation conference on December 16. It is unclear which factions will attend.