In an online statement, the front said that its fighters "simultaneously hit selected targets", which were security headquarters, military patrols, strongholds of Shiite militia groups and leading figures in the security forces as well as the Iraqi Shiite-dominated government.
The statement also said that the attacks came at a time when Iraqi security forces were intensifying security measures in Baghdad and carrying out a major offensive in the Sunni areas around Baghdad to stop ongoing insurgent attacks.
A total of 13 car bombings Monday ripped through the Shiite districts in Baghdad, killing some 41 people and wounding 151.
The Monday attacks came amid growing tension between the Sunnis and the Shiite-dominated government as the Sunnis in Iraq have been staging anti-government protests for nearly nine months against being marginalised by Nouri al-Maliki's government and "suppressed" by his Shiite-led security forces.
However, the worst security deterioration in Iraq began April 23 after the security forces cracked down on a Sunni Arab protest camp in the northern city of Hawijah.
The crackdown sparked fierce clashes across the country's predominantly Sunni provinces between the Sunni tribes and the security forces.
Iraq is witnessing its worst eruption of violence in recent years which raises fears that the country is sliding back to full blown civil conflict that peaked in 2006 and 2007 when the monthly death toll sometimes exceeded 3,000.