The Sunni Arab Association of Muslim Scholars describes Sunday's election as being tainted by a U.S.-led occupation.
The grouping of Sunni clerics says the low turnout among Sunni Arabs means that the new Iraqi assembly will not be representative and will lack the legitimacy to draft the country's constitution, something the assembly is required to do.
The Association of Muslim Scholars has been the most vocal opponent of the balloting process. It urged Iraqis to boycott the elections in protest of the U.S.-led assault last November on the Sunni city of Fallujah. The group also argued that the poll could not be fair with foreign troops on Iraqi soil.
Earlier this month, U.S. officials in Baghdad rejected the group's proposal to drop its call for a boycott in exchange for the United States to set a timetable for its troops to withdraw.
While millions of Iraqis went to the polls Sunday, early surveys show that many people in Sunni insurgent strongholds in the center of the country stayed away.
Official results from Sunday's elections have not yet been announced. But they are expected to overwhelmingly favor Iraq's Shi'ite Muslims, who make up 60 percent of the population.
Iraqi leaders worry that the election results will dangerously alienate the country's five million Sunni Arabs, who formed the backbone of Saddam Hussein's rule and are at the heart of Iraq's anti-American insurgency.
Meanwhile, officials from the Iraqi electoral commission, known as the IECI, promised to investigate claims of election irregularities that have surfaced in recent days.
On Tuesday, Iraqi Interim President Ghazi al-Yawar told reporters that he believes tens of thousands of people, including Sunnis, in the volatile northern city of Mosul and in other cities were not able to vote. Mr. Yawar says in many cases, it was because election officials did not deliver enough ballots.
"It is true many of the people could not vote because of a lack of ballots. This should be referred to the IECI. I believe that all Iraqis should be equal in their rights, no Iraqi should be prohibited from casting his vote," he said.
Politicians in northern Iraq have claimed that hundreds of thousands of people, many of them Kurdish Christians, were not able to vote because the ballots arrived too late. There are also complaints that election workers allowed some unregistered citizens to cast ballots.
Electoral commissioners say they are looking into about 100 such complaints. But they held out little hope of reopening the vote to rectify problems. Final results are due to be announced in about a week's time.