Sayyed Hazem al-Araji, imam at the Mussa al-Kazem mosque, said on Friday that the council members do not represent the Iraqi people.
"Some (Sunni) council members do not (even) represent our Sunni brethren, some of whom struggled and offered martyrs for Iraq, whereas those on the council have all been agents of America for years."
He said 'turbaned' members of the council - an allusion to Shia representatives Abdul Aziz al-Hakim and Mohammed Bahr al-Uloom - have turned into US puppets too.
"This is a governed council, not a governing council... It is an American council," said Araji, who is close to popular Shia leader Moqtada Sadr.
"Those on the council have all been agents of America for years"
Sayyed Hazem al-Araji
The Iraq Governing Council has the power to name and dismiss ministers, approve the 2004 budget and decide policy on economic and electoral reform.
It is also supposed to work out a new constitution leading to an elected, internationally-recognised Iraqi government able to take over from the council and end the military occupation.
However, final control of Iraq still rests with the US occupation-power administrator in Baghdad, Paul Bremer.