Though hand-picked by the US-led occupation administration, some of the 25-member council have expressed dismay at the behaviour of the American occupiers.
Two council members told Aljazeera that security in Iraq could only be guaranteed if Iraqis were solely in charge.
One member, Mwafaq al-Rubayee, said the occupation forces must hand over security responsibilities to the council, designated to run the war-battered country till elections are held.
Another member, Ghazi Ajeel al-Yawar said the US-led occupation forces were temperamentally ill-equipped to provide security.
Claiming that the presence of foreign troops was irksome for most Iraqis, Yawar said efforts were on so that Iraqis could take over security responsibilities soon.
He admitted that lawlessness was the biggest challenge confronting the Council at the moment.
Ever since the war, much of Iraq including capital Baghdad has slipped into anarchy and chaos.
Ordinary Iraqis have increasingly been critical of the occupation administration for failing to provide security.
On Wednesday, the occupation administration came under fire from Iraqi Turkemens as well, who staged a large and noisy demonstration protesting against their minimal representation in the governing council.
“Marginalising the Turkmen in the council does not serve the Iraqi people’s interests,” read banners as they demonstrated outside the headquarters of the US-led occupation administration in Baghdad.
The Turkmen have only one representative in the council and are demanding more berths for their community.