His Hezbollah -- unrelated to the guerrilla group of the same name in Lebanon -- was founded in 1994 and cooperated with US and British troops in the closing stages of the invasion of Iraq last year.
But his frustration with US policies appears to be pushing him away from the US-led coalition.
"I will not go back to the council until we enter a constructive discussion about Iraq ... to achieve what the Iraqi people really want and to stop the bleeding in all Iraq," al-Mohammedawi said. "I call on everybody to use the voice of wisdom and avoid violence."
Al-Khufaji, a Shiite professor of dentistry at Baghdad University, is another rising star on the Iraqi political scene. She joined the Governing Council in December.
Her conservative dress -- a black chador that covers her entire body except for the face -- makes her an exception among professional women in Iraq, most of whom wear headscarves or no traditional Islamic covering at all.
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