Allawi, who heads the secular Iraqi National List, warned there is a danger of "sectarianism" spreading throughout the Middle East.
Tensions between Sunni and Shi'ite Muslims in Iraq have been heightened since the destruction of a Shi'ite shrine in Samarra in February.
Hundreds of Iraqis have since been killed in suspected reprisal attacks.
U.S. and British officials agree sectarian tensions have increased, but do not believe Iraq is in a state of civil war.
U.S and Iraqi military stepped up their activities in the Samarra region on March 17, launching the largest air offensive since the invasion of Iraq in 2003. The U.S. military say Operation Swarmer, which is now in its third day, has so far resulted in the detention of 60 suspected insurgents and the discovery of 11 caches of weapons.
In other news, Iraqi police say U.S. troops today killed eight Iraqis after being ambushed in the town of Duluiyah, 75 kilometers north of the capital, Baghdad. They said it was not immediately clear whether the victims were militants or civilians. The U.S. military said it is checking the report.
(compiled from agency reports)