In Washington for a series of meetings hoping to drum up more support for Iraq, Maliki said that with US help his country had defeated Al-Qaeda.
But now with the vacuum created by the toppling of long-standing regimes during the Arab Spring, "the terrorists found a second chance."
His visit to the US comes as Iraq witnesses its worst violence since 2008, a surge in bloodshed that has killed more than 5,400 people this year despite several operations and tightened security measures.
"If we have had two world wars, we want a third world war against those who are killing people, killing populations, who are calling for bloodshed, for ignorance and do not want logic to govern our daily lives."
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Maliki also called for the convening of an international conference on counterterrorism to be hosted in Iraq.
His government has been criticised for not doing more to address grievances in the Sunni Arab community over alleged ill-treatment at the hands of the Shiite-led authorities.
He blamed the unrest for setting back Iraq's struggles to emerge from the dictatorship of Saddam Hussein and the bloodshed of the US invasion to rebuild its institutions, schools and homes.
Maliki will meet US President Barack Obama tomorrow at the White House to press for military equipment and greater cooperation in fighting militants.
The United States vowed yesterday to help Iraq combat terror groups, but said Baghdad needed a strategy which was not just based on increasing its military arsenal.