"We are about to make changes in the high and middle positions of those responsible for security, and the security strategy," Maliki said at a news conference in Baghdad.
"We will discuss this matter in the cabinet session tomorrow to take decisions," Maliki said, without providing further details.
"I assure the Iraqi people that they (militants) will not be able to return us to the sectarian conflict" that killed tens of thousands of people in Iraq in past years, he added.
One bomb exploded inside Al-Wardiyah mosque, while a suicide bomber detonated an explosives-rigged belt at Al-Graita mosque nearby.
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Dozens of mosques have been attacked in Iraq so far this year.
A car bomb exploded in Shaab, a Shiite area in north Baghdad, at around the time Maliki spoke, killing 12 people and wounding at least 20, officials said.
Two car bombs went off in the main southern port city of Basra, killing 13 people and wounding 48, while a wave of other bombings hit Baghdad, killing at least 11 people and wounding 102.
Iraq is home to some of the holiest sites in Shiite Islam and is visited by hundreds of thousands of foreign pilgrims every year, most of them from neighbouring Iran.
Six Sahwa anti-Al-Qaeda fighters were also killed and 27 wounded in three separate attacks north of Baghdad.
The Sahwa are made up of Sunni Arab tribesmen who joined forces with the US military against Al-Qaeda from late 2006, helping to turn the tide against the insurgency.
And a car bomb killed one person and wounded four in Rutba, a town in Anbar province, west of Baghdad, while a roadside bomb in the northern city of Mosul wounded three people.