The event's organisers had billed it as Iraq's first effort at democracy-building. But others were less receptive. One of their main criticisms has been that the conference would not be representative.
Jamal Benomar, a United Nations representative sent to help coordinate the event, says not enough is being done to make the gathering as inclusive as possible, particularly given the country's lack of experience with democracy.
The conference, described by some as a crucial step in Iraq's political transition in the run-up to elections in January, is now expected to be held in mid-August. It is expected to draw around 1000 delegates from around the country.
The Association of Muslim Scholars, Iraq's highest Sunni religious authority, has said it will not participate, and another key Sunni party, the Iraqi Islamic Party, has also decided to keep away, calling the conference "fixed".
Muqtada al-Sadr, the Shia leader who led an uprising against the occupation forces across much of southern Iraq this year, is also not sending representatives despite efforts to bring him on board.
With large chunks of the country's polity intending to stay away, some say the conference could become part of a subterfuge for those currently in power to share Iraq's political spoils.
"The security situation
in Iraq is such that it has become a part of every Iraqi's life now - if you postponed everything
for security, you'd have to postpone your life
chief of staff of the conference's preparatory committee
Delay ruled out
The UN was in favour of postponing the conference all along as it felt more time was needed to select delegates and ensure the conference was as representative as possible.
But Fouad Massoum, the Kurdish head of the preparatory committee, saw no reason for delay. Even on Thursday, his staff reiterated their commitment to go ahead with the conference.
"All Iraqis want this conference to go ahead on time, and if the Iraqi people want it, then how can we say no?" Sarko Mahmoud, Massoum's chief of staff, was quoted as saying.
"The security situation in Iraq is such that it has become a part of every Iraqi's life now - if you postponed everything for security, you'd have to postpone your life as well."
The chief task of the delegates will be the selection of a 100-member National Council. This body is expected to serve as a check on the interim government until the January elections.
The brainchild of Lakhdar Brahimi, UN special envoy, the council was designed to have many powers. It would have the right to veto legislation with a two-thirds majority, to approve Iraq's 2005 budget and to even appoint a new prime minister or president should either official resign or die in office.