Officials began compiling election results from around the country on Tuesday, but they said many citizens arrived late on Sunday to find ballot sheets had run out, possibly skewing results.
If true, the allegation that many voters were turned away could further alienate Sunnis who already say that they have been left out of the political process.
Iraq's interim President Ghazi al-Yawir said extra ballots had to be supplied to Iraq's third city of Mosul, which is mainly Sunni Arab, after twice running out on election day.
"Also, tens of thousands were unable to cast their votes because of the lack of ballots in Basra, Baghdad, and Najaf," said al-Yawir.
Deprived from voting
Iraq's Independent Electoral Commission acknowledged that some Iraqis were unable to vote because pre-election intimidation in two Sunni Arab provinces hampered preparations.
Officials admit that many Iraqis
did not vote due to intimidation
"The elections took place under difficult conditions and this undoubtedly deprived a number of citizens in a number of areas from voting," said Husain al-Hindawi, who leads the commission that organised the poll.
"The security situation was difficult in these areas and there may have been a shortage of materials in this area or that... Some centres were opened quickly, at the last moment."
Al-Hindawi said the commission was setting up an external committee made up of three Iraqi lawyers to investigate complaints. Each case would be explained in a detailed report.
Mishaan Jiburi, a candidate and national assembly member, accused the commission of deliberately supplying insufficient materials in some Sunni areas, believing few would vote.
"The elections took place under difficult conditions and this undoubtedly deprived a number of citizens in a number of areas from voting"
Husain al-Hindawi, Independent Electoral Commission
Arab voters who initially intended to boycott the polls in the ethnically-mixed city of Kirkuk apparently had changed their minds after realising they would lose to Kurds. But by the time they arrived to vote, ballot sheets were gone, he said.
"I think the decision came from Baghdad. They were concerned with keeping Sunnis out of the game," he said.
Jiburi said ballot sheets were 36,000-40,000 short in Hawija, a largely Sunni Arab area southwest of oil-rich Kirkuk.
He estimated a shortfall of 28,000 ballot papers in Baiji, a northern Sunni city, and 6000 in nearby Shirqat.
"I had a large number of voters in these areas. I am sure we will be in parliament, but if these people had been able to vote we would have won more seats," Jiburi said.
Of 5244 polling centres planned, 28 did not open, many in western Baghdad, because of poor security, the commission said.
While there were 63,000 polling booths across Iraq, there were just 33,763 independent local monitors and 622 international monitors, it added.
Final results are not expected for up to a week.
Hearts and minds
Nevertheless, Iraqi leaders stepped up efforts on Tuesday to persuade Sunni Muslims to return to the political process as the final vote count got under way.
"We must all become involved in a dialogue and reconciliation ... with everyone. All those who were not involved in violence must be part of the political process"
interim Iraqi president
Al-Yawir said all parties - except those tainted by the deadly violence that has gripped Iraq since Saddam Hussein's overthrow in April 2003 - should take part in negotiations after the election.
"We must all become involved in a dialogue and reconciliation ... with everyone. All those who were not involved in violence must be part of the political process," he said.
"There were no winners or losers" in the election he added, calling it "a victory for Iraq".
The election is likely to see Shia groups take power in Iraq.