Sunni groups felt disproportionately targeted by the ban
Shia political parties in Iraq have staged demonstrations ahead of an emergency parliamentary debate on next month's elections.
They are protesting against a court's decision to overturn a ban on candidates with alleged links to ex-President Saddam Hussein's Baath Party.
If parliament is unable to find a solution, a panel of judges will have to rule on each individual case.
This would further delay the start of campaigning.
It has already been delayed by five days to allow the emergency debate. The election itself was pushed back by nearly two months.
The court ruling, which the government has called "illegal and unconstitutional", would allow the candidates to stand for election, and be subject to investigation only after the polls.
The BBC's Gabriel Gatehouse, in Baghdad, says that although the controversial list of banned candidates straddles the sectarian divide, Sunni groups have felt disproportionately targeted.
He adds that US officials have openly expressed their concern over the blacklist, fearing that the row could damage the credibility of the election, which in turn could affect their timetable for military withdrawal.
There are still more than 100,000 American troops in Iraq.
At Sunday's demonstrations on the streets of Baghdad, Shia parties' supporters vowed to purge Baathists and chanted: "No to Baath, No to Saddam." Some voiced fears about what they saw as American interference in the electoral process.
Baathism is a form of secular Arab nationalism and was the ideology espoused by Saddam Hussein when he came to power.
Although a minority, Sunni Muslims were dominant under Saddam Hussein's rule but have since complained of being marginalised under the post-Saddam Shia-led government.