Militants including those linked to Al-Qaeda frequently target security forces and other government employees.
"It has become clear... that Iraq is subjected to a war of genocide targeting all of its components," Maliki said in his weekly address on Wednesday.
Al-Qaeda is once again "destroying the houses of citizens and killing them, and blowing up government departments," Maliki said.
But a front opposing the militant group "has begun to form in Iraq from different components... the security services and tribes and Sons of Iraq," he said, referring to anti-Al-Qaeda militiamen.
On Wednesday, gunmen killed six people in the northern city of Mosul, while five people were shot dead in and near the city the day before.
In Baghdad, a roadside bomb in the Ghazaliyah area killed at least three people and wounded 11 on Wednesday, and another killed four people and wounded at least nine in Madain, south of the capital.
Two Sahwa anti-Al-Qaeda fighters were also kidnapped and killed in the northern province of Kirkuk, and a bomb killed a policeman in Baquba, the capital of Diyala province.
Anbar province, west of Baghdad, was hit by a series of attacks late Tuesday that killed 28 people.
Four of them struck targets in and around the town of Rutba, about 110 kilometers (70 miles) from the border with Syria.
A suicide bomber detonated a tanker truck loaded with explosives at a police checkpoint east of the town, militants armed with heavy weapons struck the police station in Rutba itself and another bomber detonated a vehicle at a police checkpoint to its west.
Those attacks killed 18 police and wounded 25, while three civilians died when another suicide bomber blew up a tanker truck on a bridge west of Rutba.
Gunmen also attacked a police checkpoint Tuesday night at an entrance to Ramadi, the capital of Anbar, and another inside the city, killing seven policemen and wounding an eighth.
The violence was just the latest in a series of coordinated attacks in Anbar.
More than 550 people have now been killed this month, and more than 5,250 since the beginning of the year, according to AFP figures based on security and medical sources.
A study released this month by academics based in the United States, Canada and Iraq said nearly half a million people have died from war-related causes in Iraq since the US-led invasion of 2003.
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